Integrability, susy $SU(2)$ matter gauge theories and black holes

TL;DR

This paper extends the correspondence between integrable field theories and $SU(2)$ gauge theories with matter, providing a new non-perturbative solution and exact results for black hole quasinormal modes.

Contribution

It demonstrates that the integrability correspondence persists with added matter flavors and introduces a novel non-perturbative solution for the gauge theory.

Findings

Extended the integrability correspondence to theories with $N_f=1,2$ flavors.

Derived a new non-perturbative solution for the gauge theory.

Provided exact results for black hole quasinormal modes.

Abstract

We show that previous correspondence between some (integrable) statistical field theory quantities and periods of $SU(2)$ $\mathcal{N}=2$ deformed gauge theory still holds if we add $N_f=1,2$ flavours of matter. Moreover, the correspondence entails a new non-perturbative solution to the theory. Eventually, we use this solution to give exact results on quasinormal modes of black branes and holes.