[A more technical post follows.] In 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case that there is no other working definition of the SVMS out there, I thought I’d revisit the matter, clean up some unpublished work of mine (defining the 0B version) and develop the whole formalism much more.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 (the single asymptotic boundary loop, and the trumpet) are computing 2D SCFT partition functions (or characters), suggesting that there’s a 3D chiral supergravity dual of all of this! In certain SVMS quantities, there’s a deceptively simple plus sign where a minus sign was for the ordinary VMS. I noticed this back in 2024 and wondered about its origin. A guess was that it might make more sense in some analogue of the known VMS connection to a 2D CFT and 3D chiral gravity. I hoped the plus would relate to fermionic characters and… it turns out to be true. The matrix model is secretly computing Tr(-)^F (in the NS sector) in a 2D SCFT that I conjecture is dual to a 3D chiral supergravity theory (where there should also be 0A and 0B choices mirroring the ones I found above). The whole thing lives on a solid torus and the SCFT is on its boundary (see figure), and naturally is in terms of the channel depicted as the big loop.

This channel is S-dual to the one following boundary of the disc shown – that’s the disc that becomes the disc in JT (super)gravity in a classical limit, by the way (another reason this whole chain of relationships, first found for the VMS, is exciting) – and off one goes to connections to black hole thermodynamics, and so on.
Such supergravity setups have yet to the constructed, and the matrix model results (which should compute the same observables) give a clear roadmap for how they ought to look. By virtue of the fact that my way of constructing the matrix models gives a natural fully non-perturbative definition as well, I am fascinated by the idea that the sum over topologies (in this 3D gravity context – not generally) is given a non-perturbative completion by them. So much to explore! Anyway, I should stop here and let you read the paper.
Of course, I’ll be amused to see what lengths my esteemed colleagues will go to in order to sideline my contribution this time.
To appear today on the ArXiv.
-cvj
(*It’s a supersymmetric version of a new, special kind of string theory –Virasoro Minimal String– that was introduced in 2023 by Collier, Eberhardt, Muhlmann, and Rodriguez.)