Study of Temperature Inversion Symmetry for the Twisted Wess-Zumino

TL;DR

This paper investigates the temperature inversion symmetry in a supersymmetric ensemble at finite volume, revealing how different boundary conditions affect the symmetry of the scaled free energy.

Contribution

It demonstrates the specific antisymmetric and symmetric behaviors of the scaled free energy under temperature inversion for different boundary conditions in a supersymmetric system.

Findings

Scaled free energy is antisymmetric under temperature inversion for antiperiodic bosons and periodic fermions.

Scaled free energy is symmetric under temperature inversion for periodic bosons and antiperiodic fermions.

The symmetry properties depend on the boundary conditions of bosons and fermions in the compact dimension.

Abstract

The temperature inversion symmetry, for a non interacting supersymmetric ensemble, at finite volume, is studied. It is found that, the scaled free energy, $f(\xi)$, is antisymmetric under temperature inversion transformation, i.e. $f(\xi)=-\xi ^{d}f(\frac{1}{\xi})$. This occurs for antiperiodic bosons and periodic fermions, in the compact dimension. On the contrary, for periodic bosons and antiperiodic fermions, $f(\xi)=\xi ^{d}f(\frac{1}{\xi})$.