tag:blogger.com,1999:blog-27937484881317828962024-03-05T22:14:54.772+00:00Cross SectionsNews, rumours, and discussion about mathematics and theoretical physics.Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.comBlogger30125tag:blogger.com,1999:blog-2793748488131782896.post-55242743289225908272012-07-04T11:09:00.000+01:002012-07-04T11:09:52.478+01:00Higgsmania!<p>
CMS and ATLAS both now have conclusive evidence of a Higgs-like particle
with a mass of around $125-127$ GeV; this will be covered all over the
internet, so I won't go into details here. I will say that it's a
thrilling moment, and that we all eagerly await more data, to elucidate
the detailed properties of this particle.
</p>
<p>
But the main reason for this post is to publicly congratulate
everybody involved in this work. There are (at least) two distinct
groups of people to highlight:
<ul>
<li>
The LHC is an extraordinary machine, and has been performing
phenomenally well; this discovery is only possible now because
the machine has delivered so much integrated luminosity so quickly.
It represents an unparallelled engineering achievement, so
congratulations to the team who have worked so hard to get it to
this stage.</li></ul></p><a href="http://x-sections.blogspot.com/2012/07/higgsmania.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com2tag:blogger.com,1999:blog-2793748488131782896.post-53682473442269242752012-07-03T12:20:00.000+01:002012-07-03T12:20:09.690+01:00Professor Higgs, your boson is ready<p>
As has already been discussed extensively by many bloggers
(including <a href="http://resonaances.blogspot.co.uk/">Jester</a>,
<a href="http://www.science20.com/quantum_diaries_survivor/blog/live_blogging_july_4th_tune_here-91393">Tommaso</a>,
<a href="http://trenchesofdiscovery.blogspot.co.uk/2012/07/on-its-own-higgs-discovery-would-be.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed:+TheTrenchesOfDiscovery+%28The+Trenches+of+Discovery%29">Shaun</a>,
and especially <a href="http://www.math.columbia.edu/~woit/wordpress/">Peter
Woit</a>), CERN are holding a special seminar and press conference
tomorrow morning, to announce the latest results on the hunt
for the Higgs boson. It is widely rumoured that the evidence
of a $\sim 125$ GeV Higgs from last year has strengthened to the
point of being conclusive.
</p>
<p>
The plausibility of said rumours was only increased by a
<a href="http://www.interactions.org/cms/?pid=1031858">press
release</a>, which came out yesterday, giving the final results
from the Higgs search at the Tevatron; the paper itself is available
<a href="http://tevnphwg.fnal.gov/results/SM_Higgs_Summer_12/">here</a>.
</p><a href="http://x-sections.blogspot.com/2012/07/professor-higgs-your-boson-is-ready.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-11172629129513205752012-07-03T11:23:00.000+01:002012-07-03T11:23:45.524+01:00String Phenomenology: Days 4 & 5<p>
Well, my blogging momentum ran out towards the end of last week,
but I will wrap up the String Pheno series with some points of note
from the last two days.
</p>
<p>
In a day dominated by F-theory talks (at least in the plenary sessions),
I thought the best of the lot was from
<a href="http://www.newton.ac.uk/programmes/BSM/seminars/062811551.html">Eran
Palti</a>, who discussed 'ultra-local' model-building in F-theory. The
idea is to focus on the neighbourhood of a single point in the compact
geometry, where all the important interactions are supported.
His main point was that in many string models, we don't actually
have enough control to calculate physical coupling constants; often
an overall proportionality factor is missing, and simply assumed to
be 'of order one' (i.e. of magnitude between about .1 and 10). I think
this is a very important point; 'string phenomenology' as it stands is
a bit of a misnomer, because as far as I know, nobody has yet been able
to do an <i>honest</i> calculation of all quantities like masses and coupling
constants in a realistic string model.</p><a href="http://x-sections.blogspot.com/2012/07/string-phenomenology-days-4-5.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-10298024636433815242012-06-29T09:48:00.001+01:002012-07-03T10:39:12.611+01:00String Phenomenology: Day 3<p>
As you will have noticed if you visit this blog, I've not done a very good
job of blogging this conference. In order to keep things in order, let me
post the only thing I wrote about day 3, so I can move on to the later days!
</p>
<p>
<a href="http://www.newton.ac.uk/programmes/BSM/seminars/062709351.html">Mariana
Graña</a> discussed the consistency of putative string theory solutions
which break supersymmetry via anti-D3-branes in a warped throat (I briefly
discussed this in a
<a href="http://x-sections.blogspot.co.uk/2012/05/preprint-roundup.html">previous
post</a>). She was fairly adamant that this setup is <i>inconsistent</i>, due
to induced singularities in the three-form fluxes supporting the throat. The
most important approximation she and her collaborators have used seems to be to
'smear' the anti-D3-branes — replace the point-like branes with a continuous
charge distribution. This misses one possible resolution of the singularities,
which is polarisation of the anti-D3-branes into NS5-branes, but they have
arguments to suggest that this won't solve the problem. I doubt that the
controversy will be resolved any time soon.
</p>
<p>
(<a href="http://arxiv.org/abs/1206.6369">The latest paper</a> by Graña
et al. went on the arXiv the day after this talk.)
</p>
<p>
Edit: I suppose it's reasonable to also flag
<a href="http://www.newton.ac.uk/programmes/BSM/seminars/062717151.html">my
own talk</a>, in which I spoke about my paper from May, which I already
mentioned
<a href="http://x-sections.blogspot.co.uk/2012/05/preprint-roundup.html">here</a>.
I wasn't particularly happy with the talk, although it went okay, and I had
a fair-sized audience who seemed to pay attention, so no complaints!
</p>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-15225833521972566862012-06-27T12:17:00.000+01:002012-06-27T19:32:22.675+01:00String Phenomenology: Day 2<p>
Here are some of the highlights from day 2 of the conference, as
I saw it.
</p>
<p>
<a href="http://www.newton.ac.uk/programmes/BSM/seminars/062611551.html">Gordy
Kane</a> continued to describe his recent collaboration with Bobby Acharya
and others (see the <a href="http://x-sections.blogspot.co.uk/2012/06/string-phenomenology-day-1.html">post about day 1</a>), focussing on their prediction of the Higgs
mass. Specifically, they claim to predict that the Higgs should sit between
about 122 and 129 GeV, and most likely at about 125 GeV.
This time, the animosity towards these claims was a lot more apparent.</p><a href="http://x-sections.blogspot.com/2012/06/string-phenomenology-day-2.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com15tag:blogger.com,1999:blog-2793748488131782896.post-74917498088035487272012-06-26T10:08:00.001+01:002012-06-26T14:15:41.935+01:00String Phenomenology: Day 1<p>
Here is a brief overview of the more interesting points of day 1. I
will link to the abstracts of each talk; hopefully, in time, the same
pages will also include the slides and video from the talks.
</p>
<p>
<a href="http://www.newton.ac.uk/programmes/BSM/seminars/062509351.html">Ben
Allanach</a> kicked things off by describing some of the lates experimental
results, and what they might mean for supersymmetry (SUSY) in particular (and
hence for string model building, basically all of which is supersymmetric).
His most important points (I think) were the following:
<ul>
<li>
Discovery of a standard-model-like Higgs, with a mass of around
125 GeV, could be
<a href="http://indico.cern.ch/conferenceDisplay.py?ovw=True&confId=196564">just
around the corner</a>. In many popular realisations of SUSY breaking, a Higgs
mass of 125 GeV is right at, or just beyond, the maximum possible value,
assuming that superpartner masses are kept below several TeV.
</li>
<li>
There is an unexplained anomaly in the Tevatron data, in the
'forward-backward asymmetry' in the production of top-anti-top pairs.
The Tevatron collided protons and anti-protons, and this variable measures
the number of tops which are produced travelling in the same direction as
the initial proton, compared to the number travelling in the direction of
the anti-proton. The measured value disagrees with the standard model
prediction by something like $3\sigma$.</li></ul></p><a href="http://x-sections.blogspot.com/2012/06/string-phenomenology-day-1.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com2tag:blogger.com,1999:blog-2793748488131782896.post-38739050984172618402012-06-25T09:28:00.000+01:002012-06-25T09:28:28.580+01:00String Phenomenology 2012<p>
This week I am in Cambridge for this year's
<a href="http://www.newton.ac.uk/programmes/BSM/bsmw05.html">String
Phenomenology conference</a>, and it seems like a good excuse to do
some blogging. There are five days of what should be quite
interesting talks, and I will try to summarise and pass comment on
at least some of them every day. Watch this space!
</p>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com3tag:blogger.com,1999:blog-2793748488131782896.post-57599624317841367252012-06-01T14:17:00.000+01:002012-06-01T14:17:10.523+01:00Citation tracking<p>
I know of no good way to quantify the value of one person's contribution
to science, or indeed any other field of intellectual endeavour.
Nevertheless, people often try to do so, and the vast majority of these
efforts focus on citation counts. There are many suggestions as to what
is the most reliable indicator: total citation count, average citations
per paper, or something slightly more sophisticated, like the
<a href="http://en.wikipedia.org/wiki/H-index">h-index</a>. Needless to
say, all of these have major flaws, and tend to favour scientists who have
simply been around for a long time, or who work on popular topics, but
I get the impression that such quantities are still sometimes
used as an aid in decisions on hiring, tenure etc.
</p>
<p>
Such issues have been discussed exhaustively on the blogosphere and elsewhere
(although I'm too lazy to gather any links), and I don't really have anything
new to add. But I did want to point out that, as far as I can tell, accurate
citation data often simply aren't available.</p><a href="http://x-sections.blogspot.com/2012/06/citation-tracking.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com15tag:blogger.com,1999:blog-2793748488131782896.post-31506131397242018962012-05-24T12:41:00.000+01:002012-05-24T12:41:15.429+01:00Science and art<p>
Today's post is slightly off-topic for this blog, but I couldn't
help myself. I promise it won't happen too often. I just received,
via the departmental mailing list, an advertisment for what sounds
like quite a
<a href="http://www.tate.org.uk/whats-on/tate-modern/talks-and-lectures/mathematics-beautiful-elsewhere">
nice event</a> at the Tate Modern, in London. They are showing a
film about mathematics and mathematicians, which will be followed
by a discussion with
<a href="http://en.wikipedia.org/wiki/Michael_Atiyah">Michael Atiyah</a>
and
<a href="http://en.wikipedia.org/wiki/C%C3%A9dric_Villani">Cédric
Villani</a>, two very successful mathematicians, from different
generations, countries, and sub-fields. This is great, but it is
part of a broader series of events, going by the name
<a href="http://www.tate.org.uk/whats-on/tate-modern/eventseries/topology">
Topology</a>.
</p>
<p>
If you follow the link above, you will find some of the most
extraordinary pseudo-intellectual bullshit I have ever had the
displeasure of reading.</p><a href="http://x-sections.blogspot.com/2012/05/science-and-art_24.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com7tag:blogger.com,1999:blog-2793748488131782896.post-83623324873719322812012-05-22T13:57:00.000+01:002012-05-22T13:57:53.466+01:00Collective Marvelling<p>
I am pleased to announce that Cross Sections is now part of a small
blog network, consisting of blogs written by young researchers (meaning
PhD students and post-docs). For now, this is taking the rudimentary
form of a separate blog called
<a href="http://collectivemarvelling.blogspot.com"><i>Collective
Marvelling</i></a>, where you can find information about each of the blogs,
and snippets of the latest posts from each, linking to the main articles
themselves. There is a permanent link at the top of this page.
</p>
<p>
The name was not my idea, but I rather like it. Becoming a research
scientist is, in a sense, a way to get paid to just marvel at the natural
world!
</p>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-91983191486136927052012-05-18T10:59:00.000+01:002012-05-18T10:59:12.436+01:00How fast are neutrinos?<p>
I realise that I have not been making any effort to write at a level understandable
to non-physicists. I don't apologise for this, but I thought it was time for
another post aimed at a broader audience. There will be some equations, because
I want to be quantitative, but nothing too complicated!
</p>
<p>
Neutrinos are the most elusive of sub-atomic particles, interacting only very
weakly with other matter. In fact, according to
<a href="http://en.wikipedia.org/wiki/Neutrino#Solar">Wikipedia</a>, the total
flux of solar neutrinos (neutrinos produced by the Sun) at the distance of the Earth
is about 65 billion neutrinos per square centimetre per second(!), and these pass
straight through without us noticing them. Nevertheless, they do very occasionally
'bounce off' an atom, and this allows us to detect them, and do experiments with
them. Indeed, neutrinos made headlines last year, when the Opera experiment
claimed to measure them moving faster than light. This turned out (as most of
us expected all along) to be due to an error in the equipment, rather than a
genuine physical effect, which would have implied a breakdown of special
relativity.
</p>
<p>
Judging by various comments on blogs and the like, the whole 'superluminal
neutrino' affair did raise one puzzling point for some people. Since the 1990s,
we have known that neutrinos have mass, albeit very small, and special relativity
tells us (as we will see below), that no particle with mass can travel at the
speed of light. Yet all the news stories reported that the neutrinos were
expected to travel at the speed of light! The point is that they were expected
to travel so close to the speed of light that no difference could be measured,
and in this post, I want to explain why.
</p>
<p>
In relativity, we define the 'gamma factor' for a massive particle to be
$\gamma = \frac{E}{m\,c^2}$, where $E$ is the energy of a particle, and $m$ is its
mass.</p><a href="http://x-sections.blogspot.com/2012/05/how-fast-are-neutrinos.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com3tag:blogger.com,1999:blog-2793748488131782896.post-13256421463205750392012-05-10T10:52:00.000+01:002012-05-14T08:31:10.928+01:00Preprint roundup<p>
The sheer number of new preprints which are listed every day on the arXiv
makes it very difficult to read everything which might be of interest,
and harder still to write blog posts about every paper which one might wish
to discuss! So today I offer a short list of recent papers which have
grabbed my attention, with little in the way of commentary (and in no
particular order):
<ul>
<li>
First a bit of self-promotion. I have a new
<a href="http://arxiv.org/abs/1205.1942">paper</a> out this morning,
about Dirac gauginos in F-theory. It really only takes the first
basic steps in the study of such models, but I'm hoping it rouses
some interest in them. Dirac gauginos are one way in which reasonably
natural low-energy supersymmetry might be 'saved' from the null
results reported so far from the LHC, but as far as I can tell, they have
received zero attention from the string model building community until
now. Believe it or not, Luboš
<a href="http://motls.blogspot.co.uk/2012/05/gauginos-with-dirac-masses-and-f-theory.html">beat
me</a> to reporting this.
</li>
<br>
<li>
Also released this morning was a
<a href="http://arxiv.org/abs/1205.1798">study</a> by a number of
authors, of putative string vacua containing anti-branes in a
warped throat. This has been a widely-accepted way to break
supersymmetry at a reasonably low scale, and in a reliable way,
since the so-called <a href="http://arxiv.org/abs/hep-th/0301240">KKLT
paper</a>. The new results seem to throw doubt on the whole idea
(although I'm no expert in this subject, and I only skimmed the
paper). Usually, the anti-brane is treated in the probe
approximation, where its backreaction is ignored, and in this
formalism, it is found that the apparent singularity of the geometry
is resolved by 'polarisation' of the anti-brane. The authors claim
that this cannot occur if the backreaction is properly taken into
account, making the existence of these type of vacua somewhat more
doubtful.
</li>
</ul></p><a href="http://x-sections.blogspot.com/2012/05/preprint-roundup.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com6tag:blogger.com,1999:blog-2793748488131782896.post-81870700861897435222012-05-09T14:29:00.000+01:002012-05-09T14:40:28.315+01:00A dark matter signal from Fermi-LAT?<p>
The
<a href="http://en.wikipedia.org/wiki/Fermi_Gamma-ray_Space_Telescope">Fermi
gamma-ray telescope</a> is a space-based gamma ray observatory. Somewhat
unusually, for those of us more used to discussing collider experiments,
the data it collects is
<a href="http://fermi.gsfc.nasa.gov/ssc/data/">freely available</a> for anybody
to analyse.
Last month, Christoph Weniger, a dark matter theorist from the Max Planck
Institute in Munich, released a <a href="http://arxiv.org/abs/1204.2797">paper</a>
in which he claimed to have discovered a peak in the gamma-ray flux, possibly
corresponding to the annihilation of pairs of dark matter particles with a
mass around 130 GeV. (I'm not sure, now, why it couldn't be from decay of
a 260 GeV particle, and a quick skim over the paper hasn't enlightened me.)
One interesting aspect of this research was that the data in which Weniger
found a signal had already been analysed by the experimentalists themselves,
and they concluded that there was no signal. Weniger's trick was to focus on
those regions of the sky where models of the galaxy and its dark matter
halo predict the signal-to-noise ratio to be high. Using the full dataset
washes out the signal, hiding it in a (relatively) larger background.
</p>
<p>
This was actually discussed at length at our journal club at Oxford last
week, and the general conclusion seemed to be that the work was very interesting,
but far from convincing.</p><a href="http://x-sections.blogspot.com/2012/05/dark-matter-signal-from-fermi-lat.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com4tag:blogger.com,1999:blog-2793748488131782896.post-62258747705655699792012-04-27T15:27:00.000+01:002012-04-27T15:27:01.121+01:00How to explain the Higgs mechanism<p>
Time and again I read/hear popular-level descriptions of the
Higgs mechanism in which it is proclaimed that the Higgs field
is "like molasses", offering resistance to particles moving
through it. This is an awful analogy, and makes me cringe
every time. Even non-physicists should immediately see why:
a particle moving through molasses feels a drag force which
will ultimately bring it to rest with respect to the molasses
(in the absence of some persistent driving force). But the
Higgs field fills all of spacetime, and thanks to Galileo and
Newton, we know that in empty space, in the absence of forces,
particles move with an arbitrary constant velocity (up to the
speed limit imposed by Einstein, of course!).
</p>
<p>
The big difference is that the background value of
the Higgs field is Lorentz-invariant — it doesn't define
any absolute standard of rest.</p><a href="http://x-sections.blogspot.com/2012/04/how-to-explain-higgs-mechanism.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com3tag:blogger.com,1999:blog-2793748488131782896.post-14225495581632164412012-04-19T16:25:00.001+01:002012-04-20T08:02:25.152+01:00Miscellanea<p>
I don't seem to be finding the time to write proper blog posts,
so here is a dot-point rundown of a few things I have found
interesting lately:<br>
<ul>
<li>
Bobby Acharya, Gordon Kane, and Piyush Kumar released a
<a href="http://arxiv.org/abs/1204.2795">preprint</a> last
week in which they discuss 'generic' predictions of string
theory for low energy physics. It is well worth a look, and
represents a good review of some of the progress of the last
ten years, but the word 'generic' concerns me quite a bit in
this context; I don't even know a way to <i>define</i> a
'generic' member of a discrete set (of purported string vacua,
for example). To be fair, the paper contains a number of
caveats pointing out the various assumptions being made.
</li><br>
<li>
<a href="http://icecube.wisc.edu/">IceCube</a> is a wonderful
experiment, which uses the Antarctic ice sheet as a giant
neutrino detector. The collaboration has just published a
<a href="http://dx.doi.org/10.1038/nature11068">paper</a> in
which they report a null result in the search for neutrinos
from almost 200 gamma ray bursts, allowing them to set a limit
for neutrino production about four times below predictions.
In particular, this basically rules out gamma ray bursts as the
dominant source of very high energy cosmic rays. For a
press-release-level overview, see
<a href="http://www.interactions.org/cms/?pid=1031653">here</a>;
the BBC has also
<a href="http://www.bbc.co.uk/news/science-environment-17768771">covered</a>
the story.
</li></ul></p><a href="http://x-sections.blogspot.com/2012/04/miscellanea.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com4tag:blogger.com,1999:blog-2793748488131782896.post-15324876612378650152012-04-06T12:58:00.000+01:002012-04-07T17:43:01.730+01:00LHC back online for 2012<p>
Yesterday, CERN <a href="http://press.web.cern.ch/press/PressReleases/Releases2012/PR10.12E.html">
announced</a> that the proton-proton collisions are again underway at the LHC,
for the first time since last year. One quantitative change is that the machine
is now accelerating each beam to $4$ TeV per proton, compared to $3.5$ TeV
in 2011. (For those who might not know, $1$ TeV is equivalent, by Einstein's
famous relation $E = mc^2$, to approximately one thousand times the mass of
a proton.)
</p>
<p>
This year could be a very significant one for particle physics. If the
Higgs boson really is sitting at $\sim125$ GeV, then its discovery is
likely to be announced, and if low-energy supersymmetry is part of the
real world, then we might hope to see at least the first evidence of it.
</p><a href="http://x-sections.blogspot.com/2012/04/lhc-back-online-for-2012.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-79413060481626506632012-03-31T04:05:00.000+01:002012-03-31T04:05:48.926+01:00Hairy quantum black holes<p>
The arXiv this morning offered another
<a href="http://arxiv.org/abs/1203.6575">interesting paper</a>, this
time by Gia Dvali and Cesar Gomez. These two authors, sometimes
with collaborators, have written a number of related papers over the last
few years regarding black holes and quantum gravity. Although interested,
I'm afraid I have not taken the time to properly understand their papers,
but here is a synopsis of a couple of the relevant ones as I understand
them:
<ol>
<li>
First, there was the
<a href="http://arxiv.org/abs/1005.3497">suggestion</a> that
quantum Einstein gravity might be self-consistent in the UV,
with the naïvely-expected growth of scattering amplitudes
being softened by the production of black holes at high energies.
Trans-Planckian momentum transfer becomes ill-defined, because
horizons form before any such processes can occur. There might
therefore be no need for any fancier quantum theory of gravity.
</li>
<br>
<li>
The only other paper I want to mention is
<a href="http://arxiv.org/abs/1112.3359">this one</a>. Here they
put forward an argument that, quantum-mechnically, black holes
should be thought of as bound states of gravitons. Let me try to
summarise their argument very briefly:<br>
A gravitating system of mass $M$ sources a gravitational field
containing, they say, $N \sim \frac{M^2}{M_P^2}$ gravitons, where $M_P$
is the Planck mass. The typical wavelength of these gravitons is the
size of the gravitating source; as the source becomes more compact,
this wavelength decreases, corresponding to a greater amount of
energy being contained in the gravitational field itself. When the
source reaches its Schwarzschild radius, the original source is
(classically) hidden behind a horizon, and we can think of the entire
rest energy as residing in the gravitons. From the paper:
<blockquote>
"For us the black hole is a bound-state (Bose-condensate) of N
weakly-interacting gravitons…"
</blockquote>
<p>
They go on to explain Hawking radiation as the quantum depletion
of this condensate: interactions between the gravitons will
occasionally give one enough of a kick to escape the condensate.
Similarly, graviton interactions may pair-produce any particles in
the theory, and sometimes one of these will escape.
</p>
</li>
</ol>
I am uneasy about the ideas contained in paper 2. One
concern is the following: a Bose-Einstein condensate, consisting of some
fixed number of particles, is not much like a classical field configuration.
Every undergraduate knows about coherent states of the harmonic oscillator,
which are given by eigenstates of the annihilation operator — about as
far as one can get from a state containing a fixed number of particles.
Nevertheless, these are the 'most classical' states. Or take something less
trivial: a widely separated kink and anti-kink (so we remain in the
topologically-trivial sector) in $\lambda\phi^4$ theory in two spacetime
dimensions. Can this sensibly be treated as some bound state of $\phi$ quanta?
Even if it can, does the same reasoning apply to gravitons, considering the
rather dramatic effects which a strong gravitational field has on spacetime
(which is a fixed background for other field theories)? Perhaps these concerns
are unimportant, and I am willing to ascribe them to my own ignorance for now,
and move on to discussing the new paper.</p><a href="http://x-sections.blogspot.com/2012/03/hairy-quantum-black-holes.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-86073471043048590722012-03-28T04:35:00.001+01:002012-03-28T15:41:34.458+01:00Inflation and quantum gravity<p>
Today's arXiv listing brought an interesting new
<a href="http://arxiv.org/abs/1203.5476v1">paper</a> by
<a href="http://www-thphys.physics.ox.ac.uk/people/JosephConlon/">Joe
Conlon</a> of Oxford. In it he discusses constraints on inflation
models coming from general principles of quantum gravity.
</p>
<p>
Inflation in short is the idea that very early in its history, the
universe underwent rapid expansion by a factor of something like
a billion billion billion (or about 60 'e-folds' in the jargon of the
field). This solves certain problems of cosmology, which I don't want
to go into here. In the context of general relativity, inflation can
be achieved by a scalar field $\phi$ slowly rolling down a potential;
inflation stops when it reaches its minimum. This scalar field is called
the inflaton. Note that I am deliberately ignoring the fact that
multiple fields can play important roles in inflation; this doesn't
really matter for what I want to discuss, although see the caveat at the
end of section 2 of Joe's paper.
</p>
<p>
One variable feature of inflation models is the total distance (in field
space) which is traversed by the inflaton during inflation. There has
been some controversy about whether this can consistently be greater than
the Planck scale, because standard effective field theory arguments break
down in this case (we can, and probably should, add arbitrary operators
$\phi^k/M_P^{k-4}$ to the Lagrangian of the theory, and these all become important if
$\phi \sim M_P$, rendering the theory meaningless). This is the sort of
problem that one might hope to make some progress on by turning to
string theory…</p><a href="http://x-sections.blogspot.com/2012/03/inflation-and-quantum-gravity.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com5tag:blogger.com,1999:blog-2793748488131782896.post-90467029356327058232012-03-26T17:48:00.000+01:002012-03-26T17:49:19.864+01:00From Perimeter to U.Penn.<p>
All too soon, my visit to Perimeter came to an end yesterday, and I'm
now writing from the University of Pennsylvania, in Philadelphia. I'm here
all this week on the kind invitation of Ron Donagi, and I'll be giving a
seminar tomorrow, which will be very similar to the one I gave at PI.
This is my second visit to U.Penn., the first being last year for the
fantastic <a href="http://www.math.upenn.edu/StringMath2011/">String Math
conference.</a>
</p>
<p>
Let me mention one interesting aspect of the last week. I had the chance to
talk at some length with
<a href="http://www.blogger.com/profile/04810716508270911825">John Dixon</a>
(I recommend reading his short profile; he has had a very unconventional
career), and in particular he explained a little bit about an idea he has been
working on for several years, which he calls 'CyberSUSY'. You can find the
papers on <a href="http://arxiv.org/find/all/1/au:+dixon_john/0/1/0/all/0/1">the
arXiv</a>. It's a rather complicated idea, which I couldn't possibly explain
fully here even if I understood it, but I can outline some of the ingredients.
</p>
<p>
The theory includes a non-standard realisation of supersymmetry, and an infinite
tower of arbitrarily high-spin fields, carrying the quantum numbers of the
standard model fields (this sounds bizarre, but is reminiscent of the tower of
massive modes one finds in string theory). The supersymmetry-invariance of the
action depends on the invariance of the superpotential under certain
transformations, which are not usually considered because they do not leave the
kinetic terms invariant (and therefore are not symmetries of the theory). John's
point of view is that this ties supersymmetry together with the gauge symmetry
and multiplet structure of the standard model. Furthermore, upon the addition of
a dimensionful parameter, electroweak symmetry and supersymmetry are both broken.
</p>
<a href="http://x-sections.blogspot.com/2012/03/from-perimeter-to-upenn.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-48055509820449442272012-03-17T17:49:00.000+00:002012-03-17T17:49:30.865+00:00Seminar at Perimeter<p>
On Thursday I arrived at the <a href="http://www.perimeterinstitute.ca/">Perimeter Institute</a>
in Waterloo, Canada, for a ten day visit. It is quite a singular institution, its establishment
having been funded privately over a decade ago by
<a href="http://en.wikipedia.org/wiki/Mike_Lazaridis">Mike Lazaridis</a>, the man behind the
Blackberry.
</p>
<p>
Yesterday I gave the string seminar here, and spoke about the recent paper I discussed in
<a href="http://x-sections.blogspot.ca/2011/12/mssm-sort-of-from-heterotic-string.html">this
post</a>. Attendance was quite reasonable, and I think it went well enough. One of the
many great things about Perimeter is that they record all (I think) of the seminars given
here, and make them available for free on their website. You can check out mine
<a href="http://pirsa.org/index.php?p=speaker&name=Rhys_Davies">here</a>. It starts
about two minutes in, but nothing of import is missing. I had a look at a few minutes of
it, as I've never actually seen myself give a seminar before, and was mostly struck by
just how Australian I sound…
</p>
<p>
I'm looking forward to the next week here, after which I'll be spending a week at the
University of Pennsylvania. There are many excellent people at both institutions, so
I hope to have some interesting things to blog about.
</p>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-69198117784096929372012-03-08T11:25:00.001+00:002012-03-08T17:39:14.969+00:00More progress on anti-hydrogen<p>
To put it mildly, this blog has been rather quiet, but I hope that this post signals
a return to semi-regular blogging. Let me first quickly sum up the news in high
energy physics since December: a standard model-like Higgs is looking more and more
likely at about 125 GeV, and low-energy supersymmetry is looking less and less likely,
as the models which are still consistent with the data are getting uglier. With that
out of the way, let me turn to the subject of today's post…
</p>
<p>
In the <a href="http://x-sections.blogspot.com/2011/11/anti-matter.html">second
ever</a> entry in this blog, I discussed the ALPHA experiment at CERN, which
is designed to trap and study anti-hydrogen. As a birthday present to me
yesterday, a new
<a href="http://www.nature.com/nature/journal/vaop/ncurrent/full/nature10942.html">paper</a>
from the collaboration was published online by Nature. Last year they managed to trap
anti-hydrogen for several minutes at a time, and they are now beginning to study its
energy levels, which is the whole point of the experiment. Theory says that these
should be exactly the same as for hydrogen, and any deviation from this would be
very big news indeed.
</p>
<p>
My understanding of the experiment is as follows. They use inhomogeneous magnetic
fields to trap the atoms. The magnetic moment of an anti-hydrogen atom in its ground
state is dominated by the spin of the positron, and the experiment traps those atoms
in which the positron has one polarisation; the others escape. Once the atoms are
trapped, the team irradiates them with microwaves, tuned to a frequency which should
induce a spin-flip in some of the atoms, resulting in them escaping the trap and
annihilating in the surrounding material. They have of course performed control
experiments in which the microwaves are off-resonance.
</p>
<p>
The measurements are somewhat complicated by the external field required to trap
the atoms.</p><a href="http://x-sections.blogspot.com/2012/03/more-progress-on-anti-hydrogen.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com1tag:blogger.com,1999:blog-2793748488131782896.post-86929319048696008592011-12-07T09:43:00.001+00:002011-12-07T15:08:57.178+00:00The MSSM (sort of) from the heterotic string<p>
Today I have a <a href="http://arxiv.org/abs/1112.1097">new paper</a> out with
several collaborators, in which we construct compactifications of the heterotic
string which lead to exactly the light field content of the MSSM in four
dimensions. In itself, this is not a new achievement; it has been about six
years since such models first appeared in the literature. The difference is
that these models are obtained by deformations of the so-called 'standard
embedding' solution.
</p>
<p>
Although you probably either know this already, or won't understand it without a
lot more background, let me briefly explain what this means. In 1985, a
<a href="http://dx.doi.org/doi:10.1016/0550-3213(85)90602-9">seminal paper</a> (of
which Philip Candelas, one of my collaborators on the new work, was a co-author)
established that there is a canonical way to compactify the $E_8{\times}E_8$
heterotic string theory on any Calabi-Yau threefold $X$, leading to an
$\mathcal{N}=1$ supersymmetric theory in flat four-dimensional spacetime.
More specifically, it yields an $E_6$ gauge theory, with matter content determined
by the topology of the manifold — there are $h^{2,1}(X)$ ($h^{1,1}(X)$)
chiral multiplets in the $\mathbf{27}$ ($\mathbf{\overline{27}}$) representation, where
the notation $h^{p,q}(X)$ refers to the Hodge numbers of $X$.
</p>
<p>
There are lots of problems with the standard embedding as I've described it
so far:</p><a href="http://x-sections.blogspot.com/2011/12/mssm-sort-of-from-heterotic-string.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-88454371883099853312011-12-02T11:07:00.001+00:002011-12-02T11:40:15.831+00:00The status of the Higgs boson in 2011<p>
The Higgs boson is the last piece of the Standard Model of particle physics
which has yet to be verified by experiment. As everybody knows, discovering
this particle (or perhaps ruling out its existence) is one of the primary
goals of the LHC.
</p>
<p>
Last month, the two big collaborations focussed on discovery of new particles
at the LHC — the ATLAS and CMS teams — released combined results
from their searches for the Higgs; the punchline is the following plot:
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7JpOooPdG00xM8QxV5IfqfKdak63jSmvRGpiMPxDfil0NcXnMGwv3-QxF2y_P5VBrUB2cq0dHaUaE5vgeyfOnX1Wv681IBiLIzPLZNwFomh53tQ9u6YDG8KySYC85rqtqcE_mjuuImhc/s1600/HiggsCombinationNovember_zoom.png" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="222" width="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7JpOooPdG00xM8QxV5IfqfKdak63jSmvRGpiMPxDfil0NcXnMGwv3-QxF2y_P5VBrUB2cq0dHaUaE5vgeyfOnX1Wv681IBiLIzPLZNwFomh53tQ9u6YDG8KySYC85rqtqcE_mjuuImhc/s320/HiggsCombinationNovember_zoom.png"></a></div>
If you don't understand these "Brazil band" plots, I refer
you to a
<a href="http://www.science20.com/quantum_diaries_survivor/new_atlas_limits_higgs_mass-81880">blog entry</a>
by Tommaso Dorigo (I actually stole the picture from another of his blog
posts; I hope he doesn't mind). Roughly speaking though, we conclude that the
Higgs does not exist at mass values where the data falls below the red line.</p><a href="http://x-sections.blogspot.com/2011/12/status-of-higgs-boson-in-2011.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-90640163046039096412011-11-30T21:31:00.001+00:002011-12-01T09:20:55.064+00:00Blowing up<p>
Algebraic geometry is a subject I have had quite a lot of use for in
recent years, in my work on string compactifications, and I have come
to love it, although I am still very much a novice. It has a
reputation for being difficult and very abstract, and I think modern
algebraic geometry thoroughly deserves this. But the roots of the
subject are simple enough: it is a systematic study of the solutions
of polynomial equations (this only really becomes interesting in more
than one variable, where the solution sets can form interesting
geometric spaces). On the other hand, thanks to the 'GAGA' principle,
fairly elementary techniques of algebraic geometry are capable of
solving complicated analytic problems arising in complex geometry.
</p>
<p>
To show you that it's not all so scary, I want to present an example
of something quite familiar to physicists, and explain how it
corresponds to a common operation in algebraic geometry.</p><a href="http://x-sections.blogspot.com/2011/11/blowing-up.html#more">Read more »</a>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com0tag:blogger.com,1999:blog-2793748488131782896.post-90017266670682017412011-11-28T11:19:00.000+00:002011-11-28T15:51:54.891+00:00Now with real maths!<p>
Until now I have avoided putting any mathematical expressions into my posts, mainly because I couldn't find a nice way to go about it. But a little more searching has turned up a script which, among other things, converts simple LaTeX expressions into MathML; it is called ASCIIMathML, and I learned about it <a href="http://pleasemakeanote.blogspot.com/2008/09/how-to-post-math-equations-in-blogger.html">here</a>, and its webpage is <a href="http://www1.chapman.edu/~jipsen/mathml/asciimath.html">here</a>.
</p>
<p>
Hmm… It worked perfectly for me when I tested it, but now I am getting mixed results with Blogger's preview function. Here is a test: I would like to be able to include pretty equations like $\lim_{x \to 0} \frac{\sin(x)}{x} = 1$. Please let me know in the comments whether that is displayed correctly (note that it may initially appear as LaTeX code, but should be converted within a second or two).
</p>
<p>
Edit: For reasons I don't quite understand, ASCIIMathML wouldn't play nice (perhaps this had something to do with me storing the javascript file on my university webpage?). However, following a suggestion by Anna in the comments, formulae are now being provided by <a href="http://www.mathjax.org/">MathJax</a>, and seem to be working. Thanks Anna!
</p>Rhyshttp://www.blogger.com/profile/15520219929014063200noreply@blogger.com2