Quantum periods and TBA equations for $\mathcal{N}=2\ SU(2)\ N_f=2$ SQCD with flavor symmetry

TL;DR

This paper uses exact WKB analysis to study quantum Seiberg-Witten curves for a specific SQCD, deriving TBA equations and connecting quantum periods to the beta function of the theory.

Contribution

It introduces a novel application of WKB analysis to derive TBA equations for the quantum Seiberg-Witten curve in $ ext{SU}(2)$ SQCD with $N_f=2$ flavors, linking quantum periods to conformal field theory data.

Findings

Derived TBA equations from quantum periods

Computed the effective central charge proportional to the beta function

Formulated a Riemann-Hilbert problem for quantum periods

Abstract

We apply the exact WKB analysis to the quantum Seiberg-Witten curve for 4-dimensional $\mathcal{N} = 2\ SU(2)\ N_f=2$ SQCD with the flavor symmetry. The discontinuity and the asymptotic behavior of the quantum periods define a Riemann-Hilbert problem. We derive the thermodynamic Bethe ansatz (TBA) equations as a solution to this problem. We also compute the effective central charge of the underlying CFT, which is shown to be proportional to the one-loop beta function of the SQCD.