Sensitivity to the fermion thermal-mass prescription at three-loop HTLpt

Determine whether extending pure four-dimensional \(\mathcal N=2\) supersymmetric Yang–Mills thermodynamics to three-loop hard-thermal-loop perturbation theory reduces the sensitivity of the thermodynamic predictions to the fermion thermal-mass prescription.

Background

The paper computes the leading- and next-to-leading-order hard-thermal-loop perturbation theory (HTLpt) thermodynamic potential for pure four-dimensional $\mathcal N=2$ supersymmetric Yang–Mills theory. The thermal masses are determined variationally through gap equations, but the authors also examine an alternative prescription in which the fermion thermal mass is set to zero.

At next-to-leading order, the authors find substantial dependence of the gluon and scalar gap masses, as well as the pressure, entropy density, energy density, and trace anomaly, on the fermion-mass prescription. They propose that a three-loop HTLpt calculation could improve order-by-order stability and explicitly leave unresolved whether it will reduce this prescription dependence.