Thermal Supersymmetry in Thermal Superspace

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.