LisMath Seminar 

21/04/2022, 09:30 — 10:00 — Online
Maximilian Schwick, Instituto Superior Técnico, Universidade de Lisboa

Resurgence, Minimal String Theory and Gauge Theories

In the talk I will present the objectives and results of the two projects for my PhD. The first project constitutes the semi-classical decoding of Minimal String Theory using a generalization of Hermitian Matrix Models to Super Matrix Models. The second project revolves around understanding the Minimal String Theory - Gauge Theory Correspondence in a new way: As different expansions of one underlying Partition Function. I will start out by explaining the semi-classical decoding of (2,3) Minimal String Theory. In this context it is only known how to produce half of the non-perturbative contributions predicted by resurgence from the Minimal String Theory - or its associated Hermitian Matrix Model. Here I will quickly review Hermitian Matrix Models and then explain the super generalization. I will outline how the Super Matrix Model is capable of predicting the whole non perturbative content of Minimal String Theories. Having established how Minimal String Theories interplay with resurgent transseries expansions I will move on to understanding the Minimal String Theory - Gauge Theory Correspondence. While this correspondence is usually established via integrability methods one of my objective is to understand such a duality in a new way: By identifying the above theories as different expansions of the $\tau$ function associated to Painlevé I. We denote those expansions by rectangular Framing and Diagonal Framing. While Rectangular Framing corresponds exactly to the semi-classical decoding of Minimal String Theory discussed above, Diagonal Framing corresponds to gauge theoretic considerations. To underline the above discussion I will then present the explicit map from Rectangular to Diagonal Framing which makes the Gauge Theory Partition Function appear. To finish the talk I will present future endeavors and open problems.