Anomalously light states in super-Yang-Mills Chern-Simons theory

TL;DR

This paper investigates anomalously light bound states in three-dimensional supersymmetric Yang-Mills-Chern-Simons theory, revealing their dependence on coupling constants and the role of approximate BPS states, using SDLCQ numerical methods.

Contribution

It demonstrates the existence of anomalously light states in 3D SYM-CS theory and explores their coupling dependence, extending previous 1+1D findings to higher dimensions.

Findings

Light bound states have masses proportional to parton number and CS coupling squared.

Masses depend on the Yang-Mills coupling, unlike in lower dimensions.

Numerical results obtained via supersymmetric discrete light-cone quantization.

Abstract

Inspired by our previous finding that supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory dimensionally reduced to 1+1 dimensions possesses approximate Bogomol'nyi-Prasad-Sommerfield (BPS) states, we study the analogous phenomenon in the three-dimensional theory. Approximate BPS states in two dimensions have masses which are nearly independent of the Yang-Mills coupling and proportional to their average number of partons. These states are a reflection of the exactly massless BPS states of the underlying pure SYM theory. In three dimensions we find that this mechanism leads to anomalously light bound states. While the mass scale is still proportional to the average number of partons times the square of the CS coupling, the average number of partons in these bound states changes with the Yang-Mills coupling. Therefore, the masses of these states are not independent of the coupling. Our numerical calculations are done using supersymmetric discrete light-cone quantization (SDLCQ).