Thermal Supersymmetry in Thermal Superspace

TL;DR

This paper develops a formalism for thermal supersymmetry using thermal superspace with time-dependent Grassmann variables, establishing a consistent framework for thermal superfields and analyzing supersymmetry breaking at finite temperature.

Contribution

It introduces thermal superspace with time-dependent Grassmann variables, constructs thermal superfields, covariant derivatives, and the thermal supersymmetry algebra, and studies supersymmetry breaking in thermal systems.

Findings

Thermal supersymmetry algebra has the same structure as at zero temperature.

Thermal supersymmetry is broken in thermal systems.

Thermal superspace formalism allows consistent treatment of superfields at finite temperature.

Abstract

Thermal superspace is characterized by Grassmann variables which are time-dependent and antiperiodic in imaginary time, with a period given by the inverse temperature. The thermal superspace approach allows to define thermal superfields obeying consistent boundary conditions and to formulate a ``super-KMS'' condition for superfield propagators. Upon constructing thermal covariantizations of the superspace derivative operators, we define thermal covariant derivatives and provide a definition of thermal chiral and antichiral superfields. Thermal covariantizations of the generators of the super-Poincar\'e algebra are also constructed, and the thermal supersymmetry algebra is computed; it has the same structure as at T=0. We then investigate realizations of this thermal supersymmetry algebra on systems of thermal fields. In doing so, we observe thermal supersymmetry breaking in terms of the lifting of the mass degeneracy, and of the non-invariance of the thermal action.