Ok here goes. Been bursting to tell you this for many weeks. Ever wondered what the fully non-perturbative spectral form factor for a JT gravity model looks like? For real? Not in some special limit or simplified model? Here you go*.
Paper out on Monday! (I plan on doing a post or two about what this all means.)
–cvj
*For the experts, note that this shows both non-perturbative and strong coupling effects, which are usually hard to get at. I show how in the paper.
Can’t resist some Friday wind-down deep-dive physics humour…
-cvj
To end the week, a remarkable coincidence. This morning, I was listening to one of Wynton Marsalis’ greatest recordings, his 1983 album with the Haydn trumpet concerto in E flat major. Just found it on by accident on the radio, and found myself wondering what he’s up to these days as I have not listened to his music in a long while. Then went on a long ramble to my wife about jazz trumpeters, and classical ones, and the wonderful film score work of Terence Blanchard on all those Spike Lee films that I love, and so on. I suspect she stopped listening 20% of the way in…. Then tonight, browsing the Guardian’s website, I found – again by accident – an opinion piece from the very same Wynton Marsalis, on race and America. And it is so very well written indeed. So I thought I’d share it, before I put this all down for this evening’s big event: watching Spike Lee’s Da 5 Bloods, just out… with music by Terence Blanchard…
Enjoy.
–cvj
This Wednesday (10th June), in support of #BlackLivesMatter and the demonstrations taking part worldwide, there will be a day of action in various parts of academia to simply stop doing “business as usual” while the horrors of what is routinely done to black people at all levels of society continue.
What people choose to do on that day is up to them, but there are suggestions as a number of websites. I encourage you to go there and read what they have to say, and make up your own mind. A good start is the ShutDownStem site, and search under #ShutDownAcademia, #ShutDownSTEM and #Strike4BlackLives on social media for chatter, activity, and more resources. The Particles For Justice group, led by people in or close to my field, have also joined in to lead and encourage, and their site is here, again with lots of suggestions for types of action to get involved in.
Frankly, having seen and heard (over many cycles) a lot of rhetoric and symbolic action go nowhere on this issue, I’m not sure how I feel about this (which is partly why I’ve not posted about this for a few days since it was announced). …And I could go on at length about all the “turning points” people tell me that they can see “this time”, and how familiar it all is to me, but I won’t. I just hope that I’m wrong and that something will come of everything people are doing in their own ways. Hope is a powerful thing, and I won’t let cynicism (mine, or anyone else’s) get in the way of people trying to make a difference.
I will say that it is striking and an excellent development that people in academia, and as far removed from the everyday as particle physics, have at least recognised (this time around) that the issue is connected to them, recognized that “business as usual” is part of the problem. It’s usually easy for them to just ignore the concerns, since there are so few black people around in the corridors of academia -and especially in my field- that there’s usually nothing or nobody to remind them to stop and think about it. But of course, it’s not an accident that so few of their colleagues are black – it’s connected to the very same issue. So, great, something’s getting through, and several people are showing that they care – enough to stop what they’re doing, if just for a day, and not do “business as usual”. I respect that, and respect the people organizing this.
So have a look, and make up your own mind how/if you want to participate. Consider signing up at the Particles for Justice google page to show your support, and good luck to you.
Good luck to us all.
–cvj
(Clickable montage of some recent posts on my instagram account that might interest you. See also the twitter and Facebook accounts. Links in sidebar.)
The desire to have glitch-free online teaching and business meetings at home has driven me to do some infrastructure improvements I should have done years ago: extending the Ethernet backbone of the home network. Connecting the jacks (ethernet connectors) is a tad fiddly (but trivial), but the results are worthwhile!
In particular, it is far better (than being connected to WiFi) to have the computer connected via ethernet (had to get the appropriate dongle for my mac) when teaching via Zoom. It gives a more robust setup than you can get WiFi (unless you’re right on top of one of your WiFi transponders). Since I’ve switched to ethernet for such sessions I’ve never had even the hint of a loss of quality in my zoom session, which is important when trying to focus on the teaching subject matter, and not technology issues. I even did a radio/podcast interview the other day (online), reasonably confident that the quality was strong throughout.
There’s an ethernet connected repeater station far from the main base station, so that when it now broadcasts the network wirelessly, I there is stronger network coverage all over the house than when it was just connected over WiFi. Should have done this years ago.
-cvj
Sharing my live virtual chalkboard while online teaching using Zoom.
But the big test was this morning. Giving a two hour lecture to my General Relativity class where we were really not all in the same room, but scattered over the campus and city (and maybe beyond), while being able to maintain a live play-by-play working environment on the board, as opposed to just showing slides. Showing slides (by doing screen-sharing) is great, but for the kind of physics techniques I’m teaching, you need to be able to show how to calculate, and bring the material to life – the old “chalk and talk” that people in other fields tend to frown upon, but which is so essential to learning how to actually *think* and navigate the language of physics, which is in large part the diagrams and equations. This is the big challenge lots of people are worried about with regards going online – how do I do that? (Besides, making a full set of slides for every single lecture you might want to do For the next month or more seems to me like a mammoth task – I’d not want to do that.)
So I’ve arrived at a system that works for me, and I thought I’d share it with those of you who might not yet have found your own solution. Many of the things I will say may well be specific to me and my institution (USC) at some level of detail, but aspects of it will generalize to other situations. Adapt as applies to you.
Do share the link to this page with others if you wish to – I may well update it from time to time with more information.
Here goes:
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 slides). Then I’m more or less done.
(The facility of this old school approach is that drawing it out keeps it visual, less heavy with equations. Too many (if any) slides or long periods laden with equations (at least in physics) just aren’t so great. Also, it allows me to move these thumbnails/pages/sketches around if I need to, to sculpt the narrative. I can sit back and see if it’s all there at the end.)
(For this Harvard/MIT seminar, scheduled for Wednesday, I don’t yet know if I am going to get to give it. Wisdom about travel and gatherings is a bit uncertain right now, and things are changing as I type. Decisions on Monday. Update:- we changed it to a remote talk.)
–cvj
When looking for an excuse to have some custard, simply whip up an upside down cake built on a bit of fruit, spices, and whatnot you might have (here: apples cooked in butter, basking on caramel, with toasted walnuts, cinnamon…etc).
–cvj
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
Here’s a striking coincidence. Last Friday I was preparing to deliver a lecture on special relativity to my undergrad General Relativity class with this Hobbity thought experiment (that helps one discover Lorentz-Fitzgerald contraction), when I heard that Christopher Tolkien (the boy the Hobbit was originally written for) had died. (RIP. And thanks for the maps, the Silmarillion and so much more.)
I took the opportunity in class to pay brief tribute to him and to encourage a new generation to delve into the books, the world, and more, as expanded and illuminated for us by Tolkien the younger.
-cvj
(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:
What “nearly” AdS_2 looks like via JT gravity. The boundary wiggles, but has fixed length 1/T.
, by solving the Schwarzian dynamics for the wiggling boundary that I mentioned earlier. (The interior has a model of gravity on 
, 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: 
, where 
is the spectral density of the model. I now need to explain why everything has a subscript 0 in it in the last sentence.
, where 
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 
– 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 
where the parameter 
weights different genus surfaces. In that sum the weight of a surface is 
and 
since there’s a boundary of length 
, you may recall.
The basic Schwarzian computation mentioned above therefore gives the leading piece of the partition function, i.e., 
(A somewhat more technical post follows.)
Escher’s “Circle Limit III”, nicely illustrating (Euclidean) AdS_2 for us.
JT gravity is a model of two dimensional gravity that goes back many decades. But there’s not much going on in 2D (or (1+1) dimensions, one space and one time), I hear you cry! Well, nevertheless this turns out to be a very useful arena for studying very important quantum key properties of black holes in more realistic dimensions. Let me take a step back to unpack that.
There is a long tradition (which you might know about) of studying models of black holes in string/M-theory, in different limits and approaches, each with their own advantages and disadvantages. The simplest models are often too simple to capture some of the important features of black holes, and some models get nicely at certain aspects while having little to say about others. And of course, some of the more realistic (but still simple) black hole models are still too complicated to be directly solvable in order to reliably explore phenomena of interest.
I’d say that a certain class of models that has been discussed a lot recently has something new to offer. The prototype is something called the SYK model (Sachdev-Ye-Kitaev). It’s an even more crazy sounding starting point than 2D gravity, as it is a 1D model. There’s no space at all, just time: It is a model in (0+1) dimensions, if you like. It’s a special model of quantum mechanics, actually a bunch of 
Well, I heard people mention the SYK model increasingly over 2015 but I was thinking about too many other things (and was mostly dealing with being mostly sleep-deprived as a new dad), and so did not really pay much attention. Bandwidth issues, we’d say these days. I was happy to declare “we’ve got some of our best people on it”, and continued chipping away on other things where I could. Then in December 2017 I found myself sitting next to David Gross on a flight to the East coast (long story I forgot to blog about), and he mentioned that he’d been really excited by the SYK model and maybe I should have a look, since there’s a lot there that I’d probably like. And *still* some time went by without me clearing up bandwidth to look at any of it.
Catch up began in the Fall of last year (2019), but only after similarly missing following what was going on in a related area: JT gravity. One way of thinking about how JT gravity enters the story is to simply state that it is a holographic dual of the SYK model, in the sense of AdS/CFT, where you have a gravity theory on one side, and it is dual to a (conformally invariant) non-gravitational field theory on the other side. The key thing is that the gravitational theory has one dimension more than the field theory. I’ve spoken of such things a lot here on this blog so I won’t review, but instead let you dig a bit and find things to read in the archives. (You could put AdS/CFT in the search window, or maybe start here.)
A ball showing the AdS/CFT setup. The interior has gravity on an anti-de Sitter spacetime, the the boundary has a dual (conformal) field theory.
Important technical note: In the setup I drew above, the metric which measures spatial distances makes spacings smaller and smaller as you move out from the Click to continue reading this post
Well, you know the saying: When life hands you several apples, some blackberries, and a chunk of pastry left over from your last pie-making… you make another apple-blackberry pie, taking the opportunity to make it even better!
(No? Never heard that saying? Huh.)
-cvj
I realized recently that I’ve forgotten a great deal of my drawing skills, settling back into some clunky habits, due to zero practice. But I’m going to need them back for a project, and so will start teaching myself again. Above is a (digital) chalk doodle I did yesterday.
–cvj
