## Matrices and Gravity

So I have a confession to make. I started working on random matrix models (the large $latex N$, double-scaled variety) in 1990 or 1991, so about 30 years ago, give or take. I’ve written many papers on the topic, some of which people have even read. A subset of those have even been cited from time to time. So I’m supposed to be some kind of expert. I’ve written extensively about them here (search for matrix models and see what comes up), including posts on how exciting they are for understanding aspects of quantum gravity and black holes. So you’d think that I’d actually done the obvious thing right? Actually taken a bunch of random matrices and played with them directly. I don’t mean the fancy path integral formulation we all learn, where you take N large, find saddle points, solve for the Wigner semi-circle law that the Dyson gas of eigenvalues forms, and so forth. I don’t mean the Feynman expansion of that same path integral, and identify (following ‘t Hooft) their topology with a tessellation of random 2D surfaces. I don’t mean the decomposition into orthogonal polynomials, the rewriting of the whole problem at large $latex N$ as a theory of quantum mechanics, and so forth. No, those things I know well. I just mean do what it says on the packet: close your eyes, grab a matrix out of the bag at random, compute its eigenvalues. Then do it again. Repeat a few thousand times and see that all those things in the data that we compute those fancy ways really are true. I realized the other day that in 30 years I’d never actually done that, and (motivated by the desire to make a simple visual illustration of a point) I decided to do it, and it opened up some wonderful vistas.

Let me tell you a little more. […] Click to continue reading this post

## Full Circle

Yesterday I submitted (with collaborators Felipe Rosso and Andrew Svesko) a new paper to the arXiv that I’m very excited about! It came from one of those lovely moments when a warm flash of realisation splashed through my mind, and several fragments of (seemingly separate things) that had been floating around in my head for some time suddenly all fit together. The fit was so tight and compelling that I had a feeling of certainty that it just “had to be right”. It is a great feeling, when that happens. Of course, the details had to be worked out, and everything checked and properly developed, new tools made and some very nice computations done to unpack the consequences of the idea… and that’s what resulted in this paper! It is a very natural companion to the cluster of papers I wrote last year, particularly the ones in May and June.

What’s the story? It’s all about Jackiw-Teitelboim (JT) gravity, a kind of 2D gravity theory that shows up rather generically as controlling the low temperature physics of a wide class of black holes, including 4D ones in our universe. Understanding the quantum gravity of JT is a very nice step in understanding quantum properties of black holes. This is exciting stuff!

Ok, now I’ll get a bit more technical. Some background on all this (JT gravity, matrix models, etc), can be found in an earlier pair of posts. You might recall that in May last year I put out a paper where I showed how to define, fully non-perturbatively, a class of Jackiw-Teitelbiom (JT) supergravity theories that had been defined in 2019 in a massive paper by Stanford and Witten (SW). In effect, I showed how to build them as a particular combination of an infinite number of special “minimal string” models called type 0A strings. Those in turn are made using a special class of random matrix model based on […] Click to continue reading this post

## Shaping the Future of Scientific Conferences

This year’s big annual flagship conference in String theory, Strings 2020, ended two days ago. It was a massive success, and it was held entirely online. There were more than 2000 registered participants from all around the world, with sessions where a large portion of that number were engaged simultaneously! This conference’s attendance more usually ranges at around 300 – 400, as far as I remember, so this was a spectacular change. The success was made possible by -most importantly- the willingness of many people to take part and engage with each other to a degree that was foreign to most participants, combined with smart and tireless effort by the team of organizers in Cape Town, where the conference was originally going to be held physically. There were excellent talks (selected by the programme committee) and many illuminating discussions.

Due to the pandemic, the conference was originally going to be cancelled (or at least postponed to much later in the year), but organizer Jeff Murugan announced at relatively short notice that they were instead going to attempt to do it online on the original dates, and it is wonderful that so many people around the world engaged, instead of just shrinking away into the Covid-19 gloom.

The other major component of the success is what I want to discuss here. It was the use, sometimes in concert, of tools such as Zoom […] Click to continue reading this post

## Spectral, II

What’s that now? You want more physics teases? Ok. That dotted line is a (known) JT gravity Schwarzian spectral density. That red line? It’s the fully quantum corrected result! To all orders in topology and beyond. See my paper that appeared today on the arXiv.

(For experts: The red line is made up of about 2000 points for each of which I know the energy, and the full wave function for an associated problem. Using those I can compute lots of things, to good accuracy. One example is the full non-perturbative spectral form factor, that I showed last post.)

## Talk Prep

How do I prepare my research talks? I usually just sit down with a pencil, some paper and a cup of something warm, and I just draw/map out the story. Each box is a beat of the narrative, and ends up corresponding to one or two slides (if I’m doing … Click to continue reading this post

## New and Improved!

Updated with lots of new results! For your reading pleasure as 1912.03637 on the arXiv. (And still a swift read at 14 pages.) New results include a fascinating differential equation for spectral densities, and some lovely E=0 results. #physics #blackholes #gravity –cvj

## Black Holes and a Return to 2D Gravity! – Part II

(A somewhat more technical post follows.)

Continuing from part I: Well, I set the scene there, and so after that, a number of different ideas come together nicely. Let me list them:

[caption id="attachment_19442" align="alignright" width="250"] What “nearly” AdS_2 looks like via JT gravity. The boundary wiggles, but has fixed length 1/T.[/caption]
• Exact solution of the SYK model (or dual JT model) in that low temperature limit I mentioned before gave an answer for the partition function $latex Z(\beta)$, by solving the Schwarzian dynamics for the wiggling boundary that I mentioned earlier. (The interior has a model of gravity on $latex AdS_2$, as I mentioned before, but as we’re in 2D, there’s no local dynamics associated with that part. But we’ll see in a moment that there’s very interesting stuff to take into account there too.) Anyway, the result for the Schwarzian dynamics can be written (see Stanford and Witten) in a way familiar from standard, say, statistical mechanics: $latex Z_0(\beta)=\int dE \rho_0(E) \exp(-\beta E)$, where $latex \rho_0(E)\sim\sinh(2\pi\sqrt{E})$ is the spectral density of the model. I now need to explain why everything has a subscript 0 in it in the last sentence.
• On the other hand, the JT gravity model organises itself as a very interesting topological sum that is important if we are doing quantum gravity. First, recall that we’re working in the “Euclidean” manner discussed before (i.e., time is a spatial parameter, and so 2D space can be tessellated in that nice Escher way). The point is that the Einstein-Hilbert action in 2D is a topological counting parameter (as mentioned before, there’s no dynamics!). The thing that is being counted is the Euler characteristic of the space: $latex \chi=2-2g-b-c$, where $latex g,b,c$ are the number of handles, boundaries, and crosscaps the surface has, characterising its topology. Forget about crosscaps for now (that has to do with unorientable surfaces like a möbius strip $latex (g=0,b=1,c=1)$ – we’ll stick with orientable surfaces here). The full JT gravity action therefore has just the thing one needs to keep track of the dynamics of the quantum theory, and the partition function (or other quantities that you might wish to compute) can be written as a sum of contributions from every possible topology. So one can write the JT partition function as $latex Z(\beta)=\sum_{g=0}^\infty\hbar^{-(1-2g)}Z_g(\beta)$ where the parameter $latex \hbar$ weights different genus surfaces. In that sum the weight of a surface is $latex \hbar^{-\chi}$ and $latex b=1$ since there’s a boundary of length $latex \beta$, you may recall.

The basic Schwarzian computation mentioned above therefore gives the leading piece of the partition function, i.e., $latex g=0$, and so that’s why I put the subscript 0 on it at the outset. A big question then is what is the result for JT gravity computed on all those other topologies?!

## Black Holes and a Return to 2D Gravity! – Part I

(A somewhat more technical post follows.) Well, I think I promised to say a bit more about what I’ve been up to in that work that resulted in the paper I talked about in an earlier post. The title of my paper, “Non-perturbative JT gravity” has JT (Jackiw-Teitelbiom) gravity in … Click to continue reading this post

## Spectral

Oh, this was a recent post I did on social media that I think ought to go here too. I will try to write a longer post about the physics behind this (in involves black holes, quantum gravity, string theory, quantum chaos, and a host of other things): Were you … Click to continue reading this post

## News from the Front XIX: A-Masing de Sitter

[caption id="attachment_19335" align="alignright" width="215"] Diamond maser. Image from Jonathan Breeze, Imperial College[/caption]This is part 2 of a chat about some recent thoughts and results I had about de Sitter black holes, reported in this arxiv preprint. Part 1 is here, so maybe best to read that first.

Now let us turn to de Sitter black holes. I mean here any black hole for which the asymptotic spacetime is de Sitter spacetime, which is to say it has positive cosmological constant. This is of course also interesting since one of the most natural (to some minds) possible explanations for the accelerating expansion of our universe is a cosmological constant, so maybe all black holes in our universe are de Sitter black holes in some sense. This is also interesting because you often read here about explorations of physics involving negative cosmological constant, so this is a big change!

One of the things people find puzzling about applying the standard black hole thermodynamics is that there are two places where the standard techniques tell you there should be a temperature associated with them. There’s the black hole horizon itself, and there’s also the cosmological horizon. These each have temperature, and they are not necessarily the same. For the Schwarzschild-de Sitter black hole, for example, (so, no spins or charges… just a mass with an horizon associated with it, like in flat space), the black hole’s temperature is always larger than that of the cosmological horizon. In fact, it runs from very large (where the black hole is small) all the way (as the black hole grows) to zero, where the two horizons coincide.

You might wonder, as many have, how to make sense of the two temperatures. This cannot, for a start, be an equilibrium thermodynamics system. Should there be dynamics where the two temperatures try to equalise? Is there heat flow from one horizon to another, perhaps? Maybe there’s some missing ingredient needed to make sense of this – do we have any right to be writing down temperatures (an equilibrium thermodynamics concept, really) when the system is not in equilibrium? (Actually, you could ask that about Schwarzschild in flat space – you compute the temperature and then discover that it depends upon the mass in such a way that the system wants to move to a different temperature. But I digress.)

The point of my recent work is that it is entirely within the realm of physics we have to hand to make sense of this. The simple system described in the previous post – the three level maser – has certain key interconnected features that seem relevant:

• admits two distinct temperatures and
• a maximum energy, and
• a natural instability (population inversion) and a channel for doing work – the maser output.

My point is that these features are all present for de Sitter black holes too, starting with the two temperatures. But you won’t see the rest by staring at just the Schwarzschild case, you need to add rotation, or charge (or both). As we shall see, the ability to reduce angular momentum, or to reduce charge, will be the work channel. I’ll come back to the maximum […] Click to continue reading this post

## News from the Front, XVI: Toward Quantum Heat Engines

(The following post is a bit more technical than usual. But non-experts may still find parts helpful.)

A couple of years ago I stumbled on an entire field that I had not encountered before: the study of Quantum Heat Engines. This sounds like an odd juxtaposition of terms since, as I say in the intro to my recent paper:

The thermodynamics of heat engines, refrigerators, and heat pumps is often thought to be firmly the domain of large classical systems, or put more carefully, systems that have a very large number of degrees of freedom such that thermal effects dominate over quantum effects. Nevertheless, there is thriving field devoted to the study—both experimental and theoretical—of the thermodynamics of machines that use small quantum systems as the working substance.

It is a fascinating field, with a lot of activity going on that connects to fields like quantum information, device physics, open quantum systems, condensed matter, etc.

Anyway, I stumbled on it because, as you may know, I’ve been thinking (in my 21st-meets-18th century way) about heat engines a lot over the last five years since I showed how to make them from (quantum) black holes, when embedded in extended gravitational thermodynamics. I’ve written it all down in blog posts before, so go look if interested (here and here).

In particular, it was when working on a project I wrote about here that I stumbled on quantum heat engines, and got thinking about their power and efficiency. It was while working on that project that I had a very happy thought: Could I show that holographic heat engines (the kind I make using black holes) -at least a class of them- are actually, in some regime, quantum heat engines? That would be potentially super-useful and, of course, super-fun.

The blunt headline statement is that they are, obviously, because every stage […] Click to continue reading this post

## Event!

Well, I’m off to get six hours of sleep before the big announcement tomorrow! The Event Horizon Telescope teams are talking about an announcement of “groundbreaking” results tomorrow at 13:00 CEST. Given that they set out to “image” the event horizon of a black hole, this suggests (suggests) that they … Click to continue reading this post

## Mindscape Interview!

And then two come along at once… Following on yesterday, another of the longer interviews I’ve done recently has appeared. This one was for Sean Carroll’s excellent Mindscape podcast. This interview/chat is all about string theory, including some of the core ideas, its history, what that “quantum gravity” thing is anyway, and why it isn’t actually a theory of (just) strings. Here’s a direct link to the audio, and here’s a link to the page about it on Sean’s blog.

The whole Mindscape podcast has had some fantastic conversations, by the way, so do check it out on iTunes or your favourite podcast supplier!

I hope you enjoy it!!

## Futuristic Podcast Interview

For your listening pleasure: I’ve been asked to do a number of longer interviews recently. One of these was for the “Futuristic Podcast of Mark Gerlach”, who interviews all sorts of people from the arts (normally) over to the sciences (well, he hopes to do more of that starting with me). Go and check out his show on iTunes. The particular episode with me can be found as episode 31. We talk about a lot of things, from how people get into science (including my take on the nature vs nurture discussion), through the changes in how people get information about science to the development of string theory, to black holes and quantum entanglement – and a host of things in between. We even talked about The Dialogues, you’ll be happy to hear. I hope you enjoy listening!

(The picture? Not immediately relevant, except for the fact that I did cycle to the place the recording took place. I mostly put it there because I was fixing my bike not long ago and it is good to have a photo in a post. That is all.)

## Science Friday Book Club Wrap!

Don’t forget, today live on Science Friday we (that’s SciFri presenter Ira Flatow, producer Christie Taylor, Astrophysicist Priyamvada Natarajan, and myself) will be talking about Hawking’s “A Brief History of Time” once more, and also discussing some of the physics discoveries that have happened since he wrote that book. We’ll be taking (I think) caller’s questions too! Also we’ve made recommendations for further reading to learn more about the topics discussed in Hawking’s book.