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

TL;DR

This paper derives the maximum temperature of an ideal gas of $$ Kac-Moody fermions from a well-defined Lagrangian, revealing a temperature limit related to the coupling of the supercharge operator, similar to string theory results.

Contribution

It provides a novel derivation of the maximum temperature for Kac-Moody fermions using a Lagrangian framework, unlike previous string-based approaches.

Findings

Maximum temperature $kT_M = ||/\u03c0$ for $$ Kac-Moody fermions.

The result is obtained from a well-defined Lagrangian, ensuring theoretical consistency.

The temperature limit parallels string theory but is derived in a different context.

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 $kT_{M} = |\lambda| /\pi$, where $\lambda $ 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.