Duality symmetry of N=4 Yang-Mills theory on T^3

TL;DR

This paper investigates the spectrum of BPS states in N=4 supersymmetric U(N) Yang-Mills theory on T^3, revealing a hidden SL(5,Z) duality symmetry that relates gauge group rank and fluxes, with implications for M-theory.

Contribution

It uncovers a partially hidden SL(5,Z) duality symmetry in the BPS spectrum of N=4 Yang-Mills on T^3, linking gauge rank and fluxes, and connects to M-theory reflections.

Findings

Degeneracy of BPS bound states exhibits SL(5,Z) symmetry.

Duality transformations interchange gauge rank with fluxes.

Mapping corresponds to a reflection in M-theory directions.

Abstract

We study the spectrum of BPS states in N=4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T^3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in this model exhibits a (partially hidden) SL(5,Z) duality symmetry. Besides the electro-magnetic symmetry, this duality group also contains Nahm-like transformations that interchange the rank N of the gauge group with some of the magnetic or electric fluxes. In the M-theory interpretation, this mapping amounts to a reflection that interchanges the longitudinal direction with one of the transverse directions.