Static Charges in the Low-Energy Theory of the S-Duality Twist

TL;DR

This paper investigates the low-energy behavior of N=4 super Yang-Mills theory with S-duality twists, focusing on static charges, ground state counting, and Wilson loop actions, revealing discrepancies with existing Chern-Simons conjectures.

Contribution

It introduces a method to compute Wilson loop actions in a twisted compactification of N=4 SYM and uncovers unexpected differences from prior conjectures.

Findings

Calculated the Witten Index for ground states on a torus.

Determined Wilson loop eigenvalues in the twisted theory.

Found disagreements with previous Chern-Simons connections.

Abstract

We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.