Ground States of S-duality Twisted N=4 Super Yang-Mills Theory

TL;DR

This paper investigates the ground states of a twisted N=4 super Yang-Mills theory compactified on a circle, revealing a finite-dimensional Hilbert space with sectors related to Chern-Simons theory and connecting to (2,0)-theory boundary conditions.

Contribution

It provides a detailed analysis of the S-duality and R-symmetry twisted compactification of N=4 super Yang-Mills, identifying the structure of ground states and their relation to Chern-Simons and (2,0)-theory.

Findings

Finite-dimensional Hilbert space of ground states

Identification with Chern-Simons theory sectors

Connection to (2,0)-theory boundary conditions

Abstract

We study the low-energy limit of a compactification of N=4 U(n) super Yang-Mills theory on $S^1$ with boundary conditions modified by an S-duality and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the $T^2$ compactification of this 2+1D theory by identifying a dual weakly coupled type-IIA background. The Hilbert space of normalizable ground states is finite-dimensional and appears to exhibit a rich structure of sectors. We identify most of them with Hilbert spaces of Chern-Simons theory (with appropriate gauge groups and levels). We also discuss a realization of a related twisted compactification in terms of the (2,0)-theory, where the recent solution by Gaiotto and Witten of the boundary conditions describing D3-branes ending on a (p,q) 5-brane plays a crucial role.