Spontaneous Collapse of Supersymmetry

TL;DR

The paper demonstrates that supersymmetry necessarily breaks down in thermal states and superthermal ensembles, showing a fundamental difference from bosonic symmetry breaking.

Contribution

It proves that supersymmetry cannot be preserved in thermal or superthermal states, establishing a complete collapse of supersymmetry in such conditions.

Findings

Supersymmetry is broken in any thermal state.

Superthermal ensembles are never supersymmetric.

Supercharges cannot be defined in thermal states.

Abstract

It is shown that, if generators of supersymmetry transformations (supercharges) can be defined in a spatially homogeneous physical state, then this state describes the vacuum. Thus, supersymmetry is broken in any thermal state and it is impossible to proceed from it by ``symmetrization'' to states on which an action of supercharges can be defined. So, unlike the familiar spontaneous breakdown of bosonic symmetries, there is a complete collapse of supersymmetry in thermal states. It is also shown that spatially homogeneous superthermal ensembles are never supersymmetric.