The Weak Coupling Spectrum around Isolated Vacua in N=4 Super Yang-Mills on T^3 with any Gauge Group

TL;DR

This paper analyzes the spectrum of weakly coupled N=4 Super Yang-Mills theories on T^3 at isolated vacua, revealing a harmonic oscillator structure determined by the Lie algebra of the gauge group.

Contribution

It identifies all isolated flat connections for simple gauge groups and characterizes the low energy effective theories around these vacua.

Findings

Spectrum consists of harmonic oscillators with frequencies set by Lie algebra

All isolated flat connections for simple gauge groups are classified

Effective theories are explicitly constructed for these vacua

Abstract

The moduli space of flat connections for maximally supersymmetric Yang-Mills theories, in a space-time of the form T^3xR, contains isolated points, corresponding to normalizable zero energy states, for certain simple gauge groups G. We consider the low energy effective field theories in the weak coupling limit supported on such isolated points and find that when quantized they consist of an infinite set of harmonic oscillators whose angular frequencies are completely determined by the Lie algebra of G. We then proceed to find the isolated flat connections for all simple G and subsequently specify the corresponding effective field theories.