Surface operators, dual quivers and contours

TL;DR

This paper investigates half-BPS surface operators in 4D N=2 SU(N) gauge theories, analyzing their low-energy actions, dual quiver descriptions, and the relation between dualities and integration contours in localization.

Contribution

It establishes a connection between dual quiver descriptions of surface operators and distinct localization contours via Fayet-Iliopoulos parameters.

Findings

Dual quivers correspond to different localization contours.

Solutions of twisted chiral ring equations match localization residues.

Verification of the contour-duality correspondence through explicit mapping.

Abstract

We study half-BPS surface operators in four dimensional N=2 SU(N) gauge theories, and analyze their low-energy effective action on the four dimensional Coulomb branch using equivariant localization. We also study surface operators as coupled 2d/4d quiver gauge theories with an SU(N) flavour symmetry. In this description, the same surface operator can be described by different quivers that are related to each other by two dimensional Seiberg duality. We argue that these dual quivers correspond, on the localization side, to distinct integration contours that can be determined by the Fayet-Iliopoulos parameters of the two dimensional gauge nodes. We verify the proposal by mapping the solutions of the twisted chiral ring equations of the 2d/4d quivers onto individual residues of the localization integrand.