Hairy quantum black holes

The arXiv this morning offered another interesting paper, 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:

1. First, there was the suggestion 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.


2. The only other paper I want to mention is this one. 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:
   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:

   "For us the black hole is a bound-state (Bose-condensate) of N weakly-interacting gravitons…"

   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.

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.

Inflation and quantum gravity

Today's arXiv listing brought an interesting new paper by Joe Conlon of Oxford. In it he discusses constraints on inflation models coming from general principles of quantum gravity.

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.

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…

From Perimeter to U.Penn.

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 String Math conference.

Let me mention one interesting aspect of the last week. I had the chance to talk at some length with John Dixon (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 the arXiv. 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.

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.

Seminar at Perimeter

On Thursday I arrived at the Perimeter Institute 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 Mike Lazaridis, the man behind the Blackberry.

Yesterday I gave the string seminar here, and spoke about the recent paper I discussed in this post. 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 here. 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…

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.

More progress on anti-hydrogen

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…

In the second ever 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 paper 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.

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.

The measurements are somewhat complicated by the external field required to trap the atoms.