Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point

TL;DR

This paper investigates quantum corrections to Seiberg-Witten periods at the superconformal point in $ ext{SU}(2)$ SQCD with $N_f=1,2,3$, using the WKB method in the Nekrasov-Shatashvili limit.

Contribution

It provides explicit calculations of quantum corrections to Seiberg-Witten periods up to fourth order around the superconformal point for these theories.

Findings

Quantum corrections to periods are computed up to fourth order.

Results apply to Argyres-Douglas theories at the superconformal point.

Method can be extended to other $ ext{N}=2$ theories.

Abstract

We study the Argyres-Douglas theories realized at the superconformal point in the Coulomb moduli space of $\mathcal{N}=2$ supersymmetric $SU(2)$ QCD with $N_f=1,2,3$ hypermultiplets in the Nekrasov-Shatashvili limit of the Omega-background. The Seiberg-Witten curve of the theory is quantized in this limit and the periods receive the quantum corrections. By applying the WKB method for the quantum Seiberg-Witten curve, we calculate the quantum corrections to the Seiberg-Witten periods around the superconformal point up to the fourth order in the parameter of the Omega background.