Simulation of Dimensionally Reduced SYM-Chern-Simons Theory

TL;DR

This paper develops a supersymmetric two-dimensional theory from a three-dimensional SYM-Chern-Simons model, and uses numerical methods to analyze its bound states, revealing QCD-like features and BPS states.

Contribution

It introduces a novel dimensional reduction of SYM-Chern-Simons theory and applies SDLCQ to explore its bound state structure in 1+1 dimensions.

Findings

Bound states are very different from previous supersymmetric theories.

Low-energy states exhibit QCD-like valence structures.

Identification of BPS-like states with masses proportional to parton number.

Abstract

A supersymmetric formulation of a three-dimensional SYM-Chern-Simons theory using light-cone quantization is presented, and the supercharges are calculated in light-cone gauge. The theory is dimensionally reduced by requiring all fields to be independent of the transverse dimension. The result is a non-trivial two-dimensional supersymmetric theory with an adjoint scalar and an adjoint fermion. We perform a numerical simulation of this SYM-Chern-Simons theory in 1+1 dimensions using SDLCQ (Supersymmetric Discrete Light-Cone Quantization). We find that the character of the bound states of this theory is very different from previously considered two-dimensional supersymmetric gauge theories. The low-energy bound states of this theory are very ``QCD-like.'' The wave functions of some of the low mass states have a striking valence structure. We present the valence and sea parton structure functions of these states. In addition, we identify BPS-like states which are almost independent of the coupling. Their masses are proportional to their parton number in the large-coupling limit.