N=(1,1)super Yang-Mills theory in1+1dimensions at finite temperature

Abstract

We present a formulation of $\mathcal{N}=(1,1)$ 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 $\sqrt{{g}^{2}{N}_{\mathrm{c}}/\ensuremath{\pi}}$. 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.