[I was originally going to use the title “Back Home”, but then somehow this choice had a resonance to it that I liked. (Also reminds me of a lovely Joshua Redman album…)] So I am back in London, my home town. And since I’ve got 8 hour jet lag, I’m … Click to continue reading this post
Happy New Year!
I was greeted by great deal of green in Griffith Park today, and it was particularly lovely to look out over the whole park when I’d reached higher elevation, as the greens of various kinds stretched off in all directions, and even into the city. You’ve likely seen recent photos from me from a similar vantage point, where the dominant colours are brown and grey, so you can probably appreciate the contrast. The speed with which the green can come back in full strength never ceases to amaze me.
I’ve not done a run in this part of the park for a few weeks, for one reason or another, and so that made it all the more stark a contrast, I imagine, since there’s been a lot of rain here and there (and a lot over the last few days) and that has no doubt helped the transformation.
I’m going to take the green as an encouraging sign to press ahead (“green for go”) with this new year. There’s a great deal on my […] Click to continue reading this post
The red curve in this figure is the probability distribution of the ground state energy [latex]E=s[/latex] of the microstate spectra of quantum completions of JT gravity. Put differently (the way Wigner might have) if you ask what are all the discrete spectra that are compatible with the leading semi-classical result for quantizing JT gravity (the famous Schwarzian result for the density of states: [latex]\rho(E)=e^{S_0}(4\pi^2)^{-1}\sinh(2\pi\sqrt{E})[/latex]), this curve gives the shape of the distribution of ground states. (The blue curve is simply the associated CDF.) I first uncovered this distribution in a paper last year, with further insights and generalizations in a paper earlier this year, along with the distributions for higher energy levels that follow from it. But the exciting new result of my paper from a few weeks ago is that I have now shown that it is a solution of an ordinary differential equation (or a family of them). This allows for some powerful universal things to be said analytically about the properties of the distribution!
This is fully analogous to what happened for the well-known Tracy-Widom distribution for the largest (or smallest) energy of Gaussian random hermitian matrices. While many workers (such as Forrester) had uncovered important aspects of the distribution, and while it was known that it can be expressed as a particular Fredholm determinant, Tracy and Widom broke new ground in 1994 by showing that the distribution was governed by a well known ODE – the Painleve II equation – and in particular can be given in terms of a special solution of it studied earlier by Hastings and McLeod. The result helped forge further connections between properties of random matrix theory and several interesting areas of mathematics and mathematical physics. Furthermore, […] Click to continue reading this post
A major part of the reason I’ve been very quiet here since the last post is because I was working on a different kind of project that has in fact taken up much of my bandwidth during the last many months. This has been very welcome, as there is a … Click to continue reading this post
That Feeling
Several weeks ago, while writing up a nice set of results that extended some work I did last year, I found that I was stuck finding the right wording for how I should nuance a (seemingly minor) matter in the introductory remarks. It was partly because, frankly, I’d got bored of the standard introduction I usually make to papers on this particular subject (matrix models and 2D gravity), because I’ve written quite a few in the last two years (10-Yikes!). But I’d found a new feature that warranted a more careful way of saying the usual things, and I wanted to incorporate that aspect, and also get the Reader interested in why this aspect was interesting and worth unpacking. I played around with better ways of saying it, and still was not entirely happy. I chipped away for a bit more over a few days, and kept coming up with something less than satisfactory. I’d carry on with things in the body of the paper that would be there whatever the introduction said. Then, after coming back to the introduction and trying again, I had to stop and explore the consequences of some of the rephrasing I was doing – to make sense of the new way I was trying to say what I wanted to say.
And then it happened…
You might know that feeling: A sort of pop goes off in your head and a tingle through the whole body, and then everything looks different all of a sudden, because you realize that you’ve found a completely new way of looking at things. A way that fits *so* well and incorporates so many of the facts that it just. feels. inevitable.
That’s what happened. And then I tried to see what it would say about the larger picture of physics this all fits in, looking for a way to make it fit, or to challenge the idea to see if it breaks. Not only did not not break, it just kept making sense, and (almost like the idea itself took charge of the process) immediately offered solutions to the problems I threw at it, and readily gobbled up existing challenges that the community has been facing for a while, and explained certain things that have been a puzzle for a long time.
For the next few days I actually could not write properly at the keyboard any more. My hands were trembling every time as I utterly rebuilt the entire paper and my world view, and I could barely sit still at times.
I know this sounds like a lot, and you should know that I am open to the possibility that it is somehow wrong, but it is too compelling not to share, so that’s what my paper that came out earlier this week is all about. I am not going to repeat the paper here, but will try to highlight some features of it that form a foundation for why this changes a lot about how we think about things in this corner of physics.
Random Stuff
Let me start in the simplest way possible, as I have done in the past, with a model that is well known to many different physics communities. The Gaussian random matrix model. Random matrix models have a very long history in trying to understand complicated systems (going back to Wishart (1928), and then Wigner (1955) – physicists seem to always forget to mention Wishart, and I’m sure I’m forgetting someone else too), and they show up in all kinds for systems. There are a lot of powerful results that have been developed, and you’ve read my writings about them here to do with how they get used for understanding aspects of string theory and quantum gravity in 2D, and also in higher dimensions. The “double scaling limit” is something I’ve talked about a lot here in particular. I won’t repeat all of it here, but invite you to go and look at other posts.
[…] Click to continue reading this post
[A rather technical post follows.]
[caption id="attachment_19916" align="aligncenter" width="499"]
This figure will make more sense later in the post. It is here for decoration. Sit tight.[/caption]
For curious physicists following certain developments over the last two years, I’ll put below one or two thoughts about the new paper I posted on the arXiv a few days ago. It is called “Consistency Conditions for Non-Perturbartive Completions of JT Gravity”. (Actually, I was writing a different paper, but a glorious idea popped into my head and took over, so this one emerged and jumped out in front of the other. A nice aspect of this story is that I get to wave back at myself from almost 30 years ago, writing my first paper in Princeton, waving to myself 30 years in the future. See my last post about where I happen to be visiting now.) Anyway here are the thoughts:
Almost exactly two years ago I wrote a paper that explained how to define and construct a non-perturbatively stable completion of JT gravity. It had been defined earlier that year as a perturbative […] Click to continue reading this post
Well, I’m back.
It has been very quiet on the blog recently because I’ve been largely occupied with the business of moving. Where have I moved to? For the next academic year I’ll be on the faculty at Princeton University (as a Presidential Visiting Scholar) in the Physics department. It’s sort of funny because, as part of the business of moving forward in my research, I’ve been looking back a lot on earlier eras of my work recently (as you know from my last two year’s exciting activity in non-perturbative matrix models), and rediscovering and re-appreciating (and then enhancing and building on) a lot of the things I was doing decades ago… So now it seems that I’m physically following myself back in time too.
Princeton was in a sense my true physical first point of entry into the USA: My first postdoc was here (at the Institute for Advanced Study, nearby), and I really began […] Click to continue reading this post
For your weekend listening: Recently, I chatted with Maiken Scott, the host of the podcast The Pulse (WHYY) about many everyday aspects of energy. It was a delightful conversation and episode. Listen and share with friends! Link is here. Enjoy! -cvj
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
All of a sudden several bits of media I’ve been involved with are appearing at once. Two of them are as follows: * I had a lovely chat with Brianna Barbu of Symmetry Magazine about science, art, and science communication (particularly science advising for movies). She wrote a piece on … Click to continue reading this post
This evening at 7:30pm Central time, come to Fermilab (online) for a public talk I’ll give about shaking up how we present serious scientific ideas in books for the public. It should be fun! The information is here. -cvj
It’s pi day today! Don’t forget to celebrate! Options include walking around in circles at 1:59pm, baking a pie, eating pie, etc! Or maybe explain what pi is to somebody… I won’t list irrational behaviour as there’s a bit too much of that already… –cvj (Above image snapped from a … Click to continue reading this post
On Saturday (tomorrow), I’ll be talking with science writer Philip Ball at the Malvern Festival of Ideas! The topic will be Science and Art, and I think it will be an interesting and fun exchange. It is free, online, and starts at 5:15 pm UK time. You can click here for the details.
I’ll talk a little bit about how I came to create the non-fiction science book The Dialogues, using graphic narrative art to help frame and drive the ideas forward, and how I really wanted to re-shape what is the norm for a popular science book, where somehow using just prose to talk about serious scientific ideas has become regarded as the pinnacle of achievement – this runs counter to so many things, not the least being the fact that scientists themselves don’t just use prose to communicate with each other!
But anyway, that’s just the beginning of it all. Philip and I will talk about […] Click to continue reading this post
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
Finished a big project yesterday (more later) and so went for a big run in the park for the first time since December’s enhanced lockdown. Good to see the world, properly. -cvj
