Finite-temperature Supersymmetry as a Constrained Supergravity

Immersing a physical system in a heat bath results in the fields acquiring different properties according to their statistics. E.g., finite-temperature bosonic fields obey periodic boundary conditions, while fermionic fields satisfy antiperiodic b.c.’s. Such a distinction can be seen also at the level of the Green’s functions. Depending on the field’s statistics, thermal propagators obey either a bosonic KMS condition, or a fermionic one. Therefore, thermal effects induce a clear and mandatory distinction between bosons and fermions. As a consequence, finite temperature environments are incompatible with T = 0 supersymmetry : the supersymmetry transformation is indeed unable to take into account the distinct thermal properties that go along with different statistics.