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.
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
multicritical matrix models (ones that I co-developed 32 years or so ago) – I’d hoped to be able to do a bit more on these, but there’s where I ran out of time. Those models give a spectacularly useful set of building blocks that are particularly useful for studying JT supergravity models. (See several earlier posts on JT gravity and random matrix models.) Several “miracles” then occur as you then build up those gravity models out of them, in a way I’ve become recently very excited about, starting with the N=2 case of this recent paper, and an N=4 case I’ve worked out but not yet published.
The overall theme of this talk is the building block aspect. It is remarkable that one can do this business of building (out of multicritical components) a much wider class of gravity theories (and, it turns out, string theories – see my last two papers) that was first thought possible with these techniques decades ago. So how far can one go with this? I suspect that there’s a lot more to come.
Anyway, have a look at the KITP’s recording of the talk if some of this interests you. Some readers may also know of a pair of lectures I gave at the IAS a couple of years back on some of these techniques. This is sort of a companion to that, in that I emphasise different aspects of the basic framework. There are recordings here and here.
By the way, there was a question about recurrence relations whose answer I didn’t expand upon by the way (largely due to lack of time). See the next post for that.
–cvj
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