Category Archives: work

Computing Correlators

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[A more technical post follows]

My most recent paper, out on the arXiv today, is very exciting to me because it seems to be a genuinely new way of computing some important quantities and it is devilishly simple. So simple that I worried for months that it is all super-obvious to everyone. But another voice within me said to myself: Well if it is so obvious, why has nobody published it? Another (paranoid) voice within said: Maybe someone has published this method, and I just can’t find it in the literature…

Well, I decided that the best way to find out for sure is to put it on the arXiv and within a short time someone will email to say that I missed their important work. So, while I wait for that email (as I start writing it’s only been 30 minutes since it has been “out there”, so there’s time), let me say a few things about why I like the many results in the paper.

I was already pleased enough with the core part of the paper that I was going to write a swift four-pager about it back in February. The core point being that I figured out how to build on work I’d done in a paper back in 2024 (expanded on with followup work I did with Wasif Ahmed and Krishan Saraswat, a student and postoc). Back in 2024, I found (here) a really nice way (almost miraculous in how it worked) of writing all the corrections to the spectral density of a class of models in terms of one function [latex]u_0[/latex] and its derivatives. It was obtainable from one simple ordinary differential equation (ODE) called the Gel’fand-Dikii equation, which takes in the function [latex]u_0(x)[/latex] as input. The ODE is for a special quantity called the diagonal resolvent [latex]{\widehat R}(x,E)[/latex]. You integrate that quantity [latex]\widehat R(x,E)[/latex] with respect to [latex]x[/latex] and you’re more or less home. In general, it is a messy quantity that does not integrate to anything nice. But just when the function [latex]u(x)[/latex] obeys the “string equation” it is supposed to (as dictated by the governing model’s physics), then [latex]{\widehat R}(x,E)[/latex] is a total derivative (a seeming miracle-see later), and the corrections it gives to the density become of just the right form!

Those corrections can be called [latex]W_{g,1}(E)[/latex] where the [latex]g[/latex] is the order in perturbation theory. [latex]g=0[/latex] is leading order, [latex]g=1[/latex] is the torus, [latex]g=2[/latex] the double torus, etc. Indeed [latex]g[/latex] is the number of handles or “genus” of an associated Riemann surface. The one subscript on the other hand, corresponds to the one energy entry available when just discussing the density [latex]\rho(E)[/latex]. All the [latex]W_{g,1}[/latex] end up being written nicely in terms of a function [latex]u_0(x)[/latex] and its derivatives, evaluated at a special point.

An already nice feature (among many) of the construction was that this one ODE, recursively solved, gave rise to the [latex]W_{g,1}[/latex] of many different problems across a range, including certain random matrix models, gravity problems, intersection theory and topology, and so on. All you need to do is change the function [latex]u_0(x)[/latex]. Moreover, for this (wide) class of problems, you can compute the desired results faster and with way less machninery than other methods, such as topological recursion, which was an interesting observation. This includes very famous problems like the Weil-Petersson volumes (of the compactified moduli space [latex]\overline{\cal M}_{g,1}[/latex] of Riemann surfaces with genus [latex]g[/latex] and [latex]n=1[/latex] boundaries) and generalisations. Another nice feature is that you also get non-perturbative data beyond the genus expansion, an aspect I explored recently (in this paper) with student Joao Rodrigues, and expert in resurgence techniques.

The core breakthrough of the new paper is this: For some time, I’ve wondered how to compute correlators for more energies (amounting to multi-point correlators of [latex]\rho[/latex]) in this same way: […] Click to continue reading this post →

Nobel Prize in Physics 2025: Who/What/Why

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I started a tradition a little while back where every year we have a special departmental colloquium entitled “The Nobel Prize in Physics: Who/What/Why”. This year my job in finding speakers was made easier by having 2/3 of this years newly-minted Nobel Prize winners in physics in the Department! (Michel Devoret and John Martinis.) So our room was a bit more well-attended than normal…(hundreds and hundreds rather than dozens and dozens). Here is a recording of the event, which I was delighted to host, and there’s a celebration afterwards too. (Pls share widely!)
[…] Click to continue reading this post →

Super-Fun!

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image of completed paper, with pencilIn January 2024 I wrote a paper showing how to define the Supersymmetric Virasoro Minimal String* (SVMS) as a random matrix model, compute many of its properties, and indeed predict many aspects of its physics. This was the first time the SVMS had been constructed. Despite that, a recent paper found it necessary to specifically single out my paper disparagingly as somehow not being a string theory paper, in service of (of course) their own work trying to formulate it. Odd – and disappointingly unkind – behaviour. But I’m used to it.

Anyway, since it remains the case that there is no other working definition of the SVMS out there, I thought I’d revisit the matter, clean up some unpublished work of mine (defining the 0B version) and develop the whole formalism much more. Might be useful for people pursuing other approaches. What I thought would be at most a 10 page paper turned into a 19 page one, packed with lots of fun results.

In particular it is now clear to me how the type 0A vs 0B choices, usually done at the level of perturbative worldsheet CFT methods, show up fully at the level of matrix model string equation solutions. It is often said that random matrix model methods can rather obscure issues like worldsheet supersymmetry, making it unclear what structures pertain to what features in other approaches. That can be true, so these new observations clear show that this is not always the case. (This is true quite generally, beyond this particular family of models.)

Also (and this is lots of fun!) I demonstrate that the basic loop observables of the SVMS …. Click to continue reading this post →

A New Equation?

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Some years ago I speculated that it would nice if a certain mathematical object existed, and even nicer if it were to satisfy an ordinary differential equation of a special sort. I was motivated by a particular physical question, and it seemed very natural to me to imagine such an object… So natural that I was sure that it must already have been studied, the equation for it known. As a result, every so often I’d go down a rabbit hole of a literature dig, but not with much success because it isn’t entirely clear where best to look. Then I’d get involved with other projects and forget all about the matter.

Last year I began to think about it again because it might be useful in a method I was developing for a paper, went through the cycle of wondering, and looking for a while, then forgot all about it in thinking about other things.

Then, a little over a month ago at the end of March, while starting on a long flight across the continent, I started thinking about it again, and given that I did not have a connection to the internet to hand, took another approach: I got out a pencil and began mess around in my notebook and just derive what I thought the equation for this object should be, given certain properties it should have. One property is that it should in some circumstances reduce to a known powerful equation (often associated with the legendary 1975 work of Gel’fand and Dikii*) satisfied by the diagonal resolvent $latex {\widehat R}(E,x) {=}\langle x|({\cal H}-E)^{-1}|x\rangle$ of a Schrodinger Hamiltonian $latex {\cal H}=-\hbar^2\partial^2_x+u(x)$. It is:

$latex 4(u(x)-E){\widehat R}^2-2\hbar^2 {\widehat R}{\widehat R}^{\prime\prime}+\hbar^2({\widehat R}^\prime)^2 = 1\ .$

Here, $latex E$ is an energy of the Hamiltonian, in potential $latex u(x)$, and $latex x$ is a coordinate on the real line.

The object itself would be a generalisation of the diagonal resolvent $latex {\widehat R}(E,x)$, although non-diagonal in the energy, not the […] Click to continue reading this post →

Decoding the Universe!

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I realised just now that I entirely forgot (it seems) to post about an episode of PBS’ show Nova called “Decoding the Universe: Cosmos” which aired back in the Spring. I thought they did a good job of talking about some of the advances in our understanding that have happened over the last 50 years (the idea is that it is the 50th anniversary of the show) in areas of astrophysics and cosmology. I was a contributor, filmed at the top of Mount Wilson at the Observatory where Hubble made his famous discoveries about the size of the universe, and its expansion. I talk about some of those discoveries and other ideas in the show. Here’s a link to the “Decoding the Universe” site. (You can also find it on YouTube.)

If you follow the link you’ll notice another episode up there: “Decoding the Universe: Quantum”. That’s a companion they made, and it focuses on understanding in quantum physics, connecting it to things in the everyday world. and also back to black holes and things astrophysical and cosmological. It also does a good job of shining a light on many concepts.

I was also a contributor to this episode, and it was a real delight to work with them in a special role: I got to unpack many of the foundational quantum mechanical concepts (transitions in atoms, stimulated emission, tunnelling, etc) to camera by doing line drawings while I explained – and kudos […] Click to continue reading this post →

When Worlds Collide…

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This morning I had a really fantastic meeting with some filmmakers about scientific aspects of the visuals (and other content) for a film to appear on your screens one day, and also discussed finding time to chat with one of the leads in order to help them get familiar with aspects of the world (and perhaps mindset) of a theoretical physicist. (It was part of a long series of very productive meetings about which I can really say nothing more at the current time, but I’m quite sure you’ll hear about this film in the fullness of time.)

Then a bit later I had a chat with my wife about logistical aspects of the day so that she can make time to go down to Los Angeles and do an audition for a role in something. So far, so routine, and I carried on with some computations I was doing (some lovely clarity had arrived earlier and various piece of a puzzle fell together marvellously)…

But then, a bit later in the morning while doing a search, I stumbled upon some mention of the recent Breakthrough Prize ceremony, and found the video below […] Click to continue reading this post →

Catching Up

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Since you asked, I should indeed say a few words about how things have been going since I left my previous position and moved to being faculty at the Santa Barbara Department of Physics.

It’s Simply Wonderful!

(Well, that’s really four I suppose, depending upon whether you count the contraction as one or two.)

Really though, I’ve been having a great time. It is such a wonderful department with welcoming colleagues doing fantastic work in so many areas of physics. There’s overall a real feeling of community, and of looking out for the best for each other, and there’s a sense that the department is highly valued (and listened to) across the wider campus. From the moment I arrived I’ve had any number of excellent students, postdocs, and faculty knocking on my door, interested in finding out what I’m working on, looking for projects, someone to bounce an idea off, to collaborate, and more.

We’ve restarted the habit of regular (several times a week) lunch gatherings within the group, chatting about physics ideas we’re working on, things we’ve heard about, papers we’re reading, classes we’re teaching and so forth. This has been a true delight, since that connectivity with colleagues has been absent in my physics life for very many years now and I’ve sorely missed it. Moreover, there’s a nostalgic aspect to it as well: This is the very routine (often with the same places and some of the same people) that I had as a postdoc back in the mid 1990s, and it really helped shape the physicist I was to become, so it is a delight to continue the tradition.

And I have not even got to mentioning the Kavli Institute for Theoretical Physics (KITP) [….] Click to continue reading this post →

Multicritical Matrix Model Miracles

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Well, that was my title for my seminar last Thursday at the KITP. My plan was to explain more the techniques behind some of the work I’ve been doing over the last few years, in particular the business of treating multicritical matrix models as building blocks for making more complicated theories of gravity.

chalkboard from KITP seminar

The seminar ended up being a bit scattered in places as I realised that I had to re-adjust my ambitions to match limitations of time, and so ended up improvising here and there to explain certain computational details more, partly in response to questions. This always happens of course, and I sort of knew it would at the outset (as was clear from my opening remarks of the talk). The point is that I work on a set of techniques that are very powerful at what they do, and most people of a certain generation don’t know those techniques as they fell out of vogue a long time ago. In the last few years I’ve resurrected them and developed them to a point where they can now do some marvellous things. But when I give talks about them it means I have a choice: I can quickly summarise and then get to the new results, in which case people think I’m performing magic tricks since they don’t know the methods, or I can try to unpack and review the methods, in which case I never get to the new results. Either way, you’re not likely to get people to dive in and help move the research program forward, which should be the main point of explaining your results. (The same problem occurs to some extent when I write papers on this stuff: short paper getting swiftly to the point, or long paper laying out all the methods first? The last time I did the latter, tons of new results got missed inside what people thought was largely just a review paper, so I’m not doing that any more.)

Anyway, so I ended up trying at least to explain what (basic) multicritical matrix models were, since it turns out that most people don’t know these days what the (often invoked) double scaling limit of a matrix model really is, in detail. This ended up taking most of the hour, so I at least managed to get that across, and whet the appetite of the younger people in the audience to learn more about how this stuff works and appreciate how very approachable these techniques are. I spent a good amount of time trying to show how to compute everything from scratch – part of the demystifying process.

I did mention (and worked out detailed notes on) briefly a different class of […] Click to continue reading this post →

Living in the Matrix – Recent Advances in Understanding Quantum Spacetime

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It has been extremely busy in the ten months or so since I last wrote something here. It’s perhaps the longest break I’ve taken from blogging for 20 years (gosh!) but I think it was a healthy thing to do. Many readers have been following some of my ocassional scribblings … Click to continue reading this post →

A Return (Again)

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About two years ago I wrote a post entitled “A Return”, upon moving to Princeton for a year (I was a Presidential Visiting Scholar at the Physics department). I reflected upon the fact that it was a return to a significant place from my past, where I’d been transformed in so many ways. Princeton was the first place I visited (not counting airports) in the USA, the location of my first postdoctoral appointment (at the Institute for Advanced Study (IAS)), and its was there that I did a deep enriching dive into the hubbub of Theoretical Physics, at one of the very top places in the world to do so.

Coastal view from UCSB campusAfter that, I moved West, to Santa Barbara, where my next postdoc position was at the Institute for Theoretical Physics at the University of California Santa Barbara (UCSB), now called the KITP. I was very lucky to be able to go from one top place to another, and (as I’ve recently talked about in a BBC interview here) additionally, my field was in a delicious turmoil of activity and discovery. I was able to be a part of the maelstrom (the “Second Superstring Revolution”, and all the gifts it gave us, including better understanding of the role in quantum gravity of extended objects beyond strings (such as D-branes), the physics of quantum black holes, the tools to unlock the holographic nature of quantum gravity more generally (through AdS/CFT), and so on. (I’ve blogged about many of these topics here, so use the search tool for more.)

I’ve been known to say that Princeton was the place where I found my physics voice (Edward Witten was a key guide at that time). Well, to continue the theme, Santa Barbara (with its wonderful research group made up of people from both the KITP and the wider Physics Department) was the place where I started to learn how to use that voice to sing (with the guidance of Joe Polchinski (who sadly passed away a few years ago)).

Well, as you may be guessing after that long introduction, I’m doing “A Return” again, but this time not with some boxes and suitcases of things for a year’s stay: I can now announce that I’ll be leaving the University of Southern California (USC) and (as of 1st July 2023) joining […] Click to continue reading this post →

The Life Scientific Interview

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After doing a night bottle feed of our youngest in the wee hours of the morning some nights earlier this week, in order to help me get back to sleep I decided to turn on BBC Sounds to find a programme to listen to… and lo and behold, look what had just aired live! The programme that I’d recorded at Broadcasting House a few weeks ago in London.

So it is out now. It is an episode of Jim Al-Khalili’s excellent BBC Radio 4 programme “The Life Scientific”. The show is very much in the spirit of what (as you know) I strive to do in my work in the public sphere (including this blog): discuss the science an individual does right alongside aspects of the broader life of that individual. I recommend listening to […] Click to continue reading this post →

What a Week!

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Some Oxford scenesI’m sitting, for the second night in a row, in a rather pleasant restaurant in Oxford, somewhere on the walk between the physics department and my hotel. They pour a pretty good Malbec, and tonight I’ve had the wood-fired Guinea Fowl. I can hear snippets of conversation in the distance, telling me that many people who come here are regulars, and that correlates well with the fact that I liked the place immediately last night and decided I’d come back. The friendly staff remembered me and greeted me like a regular upon my return, which I liked. Gee’s is spacious with a high ceiling, and so I can sit away from everyone in a time where I’d still rather not be too cavalier with regards covid. On another occasion I might have sought out a famous pub with some good pub food and be elbow-to-elbow with students and tourists, but the phrase “too soon” came to mind when I walked by such establishments and glanced into the windows.

However, I am not here to do a restaurant review, although you might have thought that from the previous paragraph (the guinea fowl was excellent though, and the risotto last night was tasty, if a tiny bit over-salted for my tastes). Instead I find myself reflecting on […] Click to continue reading this post →