Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groups

TL;DR

This paper computes the spectrum of bound states in N=4 SYM on T^3 for Spin(2n) and exceptional groups, revealing insights into their S-duality properties and the structure of their moduli space.

Contribution

It extends previous work by classifying bound states for even-dimensional spin and exceptional gauge groups, confirming S-duality constraints.

Findings

Bound states are characterized by discrete 't Hooft fluxes.

Spectrum matches S-duality predictions in complex cases.

Results include new classifications for Spin(2n) and exceptional groups.

Abstract

The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes. At weak coupling, the wave-functions of these states are supported near points in the moduli space of flat connections where the unbroken gauge group is semi-simple. The number of such states is related to the number of normalizable bound states at threshold in the supersymmetric matrix quantum mechanics with 16 supercharges based on this unbroken group. Mathematically, the determination of the spectrum relies on the classification of almost commuting triples with semi-simple centralizers. We complete the work begun in a previous paper, by computing the spectrum of bound states in theories based on the even-dimensional spin groups and the exceptional groups. The results satisfy the constraints of S-duality in a rather non-trivial way.