Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theory

TL;DR

This paper analyzes the low-energy spectrum of minimally supersymmetric Yang-Mills-Chern-Simons theory on a small two-torus, focusing on zero-mode dynamics and their energy spectrum for various gauge groups.

Contribution

It provides a detailed determination of the zero-mode spectrum in supersymmetric Yang-Mills-Chern-Simons theory on a small torus, including cases with different gauge groups.

Findings

Zero-modes decouple from non-zero modes on small torus.

Energy spectrum is quantized in multiples of the square of the coupling constant.

Explicit examples for different gauge groups are worked out.

Abstract

We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states with energies that are given by multiples of the square of the coupling constant. We discuss the determination of this low-energy spectrum, both for simply connected gauge groups and for gauge groups of adjoint type, with a few examples worked out in detail.