Realizations of Thermal Supersymmetry

We investigate realizations of supersymmetry at finite temperature in terms of thermal superfields, in a thermally constrained superspace: the Grassmann coordinates are promoted to be time-dependent and antiperiodic, with a period given by the inverse temperature. This approach allows to formulate a Kubo-Martin-Schwinger (KMS) condition at the level of thermal superfield propagators. The latter is proven directly in thermal superspace, and is shown to imply the correct (bosonic and fermionic) KMS conditions for the component fields. In thermal superspace, we formulate thermal covariant derivatives and supercharges and derive the thermal super-Poincar\'e algebra. Finally, we briefly investigate field realizations of this thermal supersymmetry algebra, focussing on the Wess-Zumino model. The thermal superspace formalism is used to characterize the breaking of global supersymmetry at finite temperature.