Wave functions and properties of massive states in three-dimensional supersymmetric Yang-Mills theory

TL;DR

This paper uses supersymmetric discrete light-cone quantization to analyze the spectrum of massive states in 3D supersymmetric Yang-Mills theory, revealing two distinct sectors with different properties and behaviors.

Contribution

It provides a detailed numerical study of the bound states in supersymmetric Yang-Mills theory on a compact space, highlighting the spectrum division and properties of states at various couplings.

Findings

Spectrum divides into two disjoint sectors.

States in one sector are well-behaved at intermediate coupling.

Masses in the other sector grow with the transverse cutoff at strong coupling.

Abstract

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills 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. We present an overview of all the massive states of this theory, and we see that the spectrum divides into two distinct and disjoint sectors. In one sector the SDLCQ approximation is only valid up to intermediate coupling. There we find a well defined and well behaved set of states, and we present a detailed analysis of these states and their properties. In the other sector, which contains a completely different set of states, we present a much more limited analysis for strong coupling only. We find that, while these state have a well defined spectrum, their masses grow with the transverse momentum cutoff. We present an overview of these states and their properties.