Rigid surface operators and S-duality: some proposals

TL;DR

This paper investigates the behavior of rigid surface operators in N=4 supersymmetric Yang-Mills theories with SO(n) and Sp(2n) gauge groups, proposing how S-duality maps these operators, especially unipotent and semisimple types.

Contribution

It provides explicit proposals for the S-duality transformation of unipotent and certain semisimple surface operators in these theories.

Findings

Proposed explicit S-duality map for unipotent surface operators.

Discussed potential S-duality relations for subclasses of semisimple operators.

Enhanced understanding of surface operator dualities in gauge theories.

Abstract

We study surface operators in the N=4 supersymmetric Yang-Mills theories with gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these theories have a class of rigid surface operators which are expected to be related by S-duality. The rigid surface operators are of two types, unipotent and semisimple. We make explicit proposals for how the S-duality map should act on unipotent surface operators. We also discuss semisimple surface operators and make some proposals for certain subclasses of such operators.