The deconfined phase of ${\cal N}=1$ SUSY Yang-Mills: bound states and the equation of state

TL;DR

This paper investigates the deconfined phase of ${ m N}=1$ supersymmetric Yang-Mills theory, revealing bound states of gluons and gluinos up to 1.4 times the critical temperature and showing the equation of state closely resembles non-supersymmetric Yang-Mills.

Contribution

It introduces a nonperturbative T-matrix approach to study bound states and the equation of state in ${ m N}=1$ SUSY Yang-Mills, demonstrating the existence of bound states and gauge group independence.

Findings

Bound states of gluons and gluinos exist up to 1.4 $T_c$.

The equation of state is nearly gauge-group independent.

The orientifold equivalence holds at the level of the equation of state.

Abstract

The properties of the deconfined phase of ${\cal N}=1$ supersymmetric Yang-Mills theory in $(3+1)$-dimensions are studied within a $\cal T$-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1-5)~$T_c$, where the interaction are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 $T_c$ for any gauge group. The equation of state is given for SU($N$) and $G_2$; it is found to be nearly independent of the gauge group and very close to that of non-supersymmetric Yang-Mills when normalized to the Stefan-Boltzmann pressure and expressed as a function of $T/T_c$. Finally the orientifold equivalence is shown to hold at the level of the equation of state and its accuracy at $N=3$ is shown to be very good.