Surface operators in 5d gauge theories and duality relations

TL;DR

This paper investigates half-BPS surface operators in 5d gauge theories, using localization and duality relations to analyze their properties and the effects of Chern-Simons levels on their instanton partition functions.

Contribution

It introduces a method to compute the twisted chiral superpotential for surface operators in 5d theories and explores duality relations between different quiver realizations.

Findings

Derived constraints on Chern-Simons levels for contour independence.

Calculated twisted chiral superpotential using localization.

Identified duality relations between quiver theories for the same surface operator.

Abstract

We study half-BPS surface operators in 5d N=1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.