# Surface operators in N=2 SQCD and Seiberg Duality

## TL;DR

This paper investigates half-BPS surface operators in N=2 supersymmetric SU(N) gauge theories, revealing how Seiberg duality corresponds to contour deformations in localization integrals and modifies duality rules with non-perturbative effects.

## Contribution

It establishes a detailed mapping between Seiberg duality in 2d/4d quiver gauge theories and contour deformations in localization, introducing new duality rules dependent on the 4d gauge coupling.

## Key findings

- Seiberg duality corresponds to contour deformations in localization integrals.
- Modified duality rules include non-perturbative terms depending on the gauge coupling.
- Matching of low energy effective twisted superpotentials for dual quivers.

## Abstract

We study half-BPS surface operators in N=2supersymmetric asymptotically conformal gauge theories in four dimensions with SU(N) gauge group and 2N fundamental flavours using localization methods and coupled 2d/4d quiver gauge theories. We show that contours specified by a particular Jeffrey-Kirwan residue prescription in the localization analysis map to particular realizations of the surface operator as flavour defects. Seiberg duality of the 2d/4d quivers is mapped to contour deformations of the localization integral which in this case involves a residue at infinity. This is reflected as a modified Seiberg duality rule that shifts the Lagrangian of the purported dual theory by non-perturbative terms. The new rules, that depend on the 4d gauge coupling, lead to a match between the low energy effective twisted chiral superpotentials for any pair of dual 2d/4d quivers.