Non-perturbative studies of N=2 conformal quiver gauge theories

TL;DR

This paper provides a detailed non-perturbative analysis of N=2 superconformal quiver gauge theories in four dimensions, utilizing Seiberg-Witten curves, the AGT correspondence, and localization methods to compute the prepotential.

Contribution

It establishes a precise parameter map and explicit non-perturbative prepotential expressions for N=2 conformal quiver gauge theories, including cases with Omega-backgrounds.

Findings

Explicit Seiberg-Witten curve descriptions for n=1,2 cases

Validated prepotential calculations against Nekrasov localization results

Enhanced understanding of the parameter-physical quantity correspondence

Abstract

We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n=1,2, also in the presence of an Omega-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotential a la Nekrasov using localization methods.