Maximum temperature for an Ideal Gas of $\hat U(1)$ Kac-Moody Fermions

Abstract

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the $\hat U(1)$ case is shown to have a maximum temperature $kT_{M} = |λ| /π$, where $λ$ is the coupling of the super charge operator $G_0 $ to the fermions. This result is similar to the case of strings but unlike strings the result is obtained from a well-defined lagrangian.