BPS States in Omega Background and Integrability

TL;DR

This paper explores the role of BPS states, topological defects, and integrability in N=2 supersymmetric gauge theories with Omega background, connecting dualities, effective theories, and the AGT correspondence.

Contribution

It provides a detailed analysis of BPS states and their associated defects in the Omega background, linking 4d/2d dualities and integrable models in the NS limit.

Findings

Identification of topological defects in Omega background

Connection between 4d/2d dualities and integrable models

Verification of AGT correspondence in the NS limit

Abstract

We reconsider string and domain wall central charges in N=2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory - vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in N=2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.