Properties of the Bound States of Super-Yang-Mills-Chern-Simons Theory

TL;DR

This paper uses supersymmetric discrete light-cone quantization to study bound states in supersymmetric Yang-Mills-Chern-Simons theory on a compact space, revealing spectrum properties, structure functions, and special states at various couplings.

Contribution

It introduces a finite, supersymmetry-preserving numerical approach to analyze SYM-CS bound states and explores their spectrum, wave functions, and Kaluza-Klein states at different coupling regimes.

Findings

Spectrum analyzed at free, weak, and strong coupling.

Identified properties of Kaluza-Klein states and their strong coupling behavior.

Discovered anomalously light states related to BPS states.

Abstract

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory on R x S^1 x S^1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. The Chern-Simons term is introduced here to provide masses for the particles while remaining totally within a supersymmetric context. We examine the free, weak and strong-coupling spectrum. The transverse direction is discussed as a model for universal extra dimensions in the gauge sector. The wave functions are used to calculate the structure functions of the lowest mass states. We discuss the properties of Kaluza-Klein states and focus on how they appear at strong coupling. We also discuss a set of anomalously light states which are reflections of the exact Bogomol'nyi-Prasad-Sommerfield states of the underlying SYM theory.