N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature

TL;DR

This paper investigates the finite-temperature behavior of N=(1,1) super Yang-Mills theory in 1+1 dimensions, revealing an exponential growth in the density of states and identifying a Hagedorn temperature through numerical spectrum analysis.

Contribution

The study introduces a numerical approach using SDLCQ to analyze the spectrum and thermodynamics of the theory at finite temperature, highlighting the existence of a Hagedorn temperature.

Findings

Density of states grows exponentially

Identified a Hagedorn temperature slightly below 1

Thermodynamics dominated by massless states below Hagedorn temperature

Abstract

We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions at finite temperature. The partition function is constructed by finding a numerical approximation to the entire spectrum. We solve numerically for the spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the large-N_c approximation and calculate the density of states. We find that the density of states grows exponentially and the theory has a Hagedorn temperature, which we extract. We find that the Hagedorn temperature at infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2). We use the density of states to also calculate a standard set of thermodynamic functions below the Hagedorn temperature. In this temperature range, we find that the thermodynamics is dominated by the massless states of the theory.