Symmetry Breaking for Matter Coupled to Linearized Supergravity From the Perspective of the Current Supermultiplet

TL;DR

This paper investigates how spontaneous symmetry breaking in supersymmetric matter coupled to linearized supergravity induces gravitino mass terms, especially under conditions of zero or nonzero energy momentum tensor vacuum expectation values, revealing new structures related to CP violation.

Contribution

It introduces a generalized gravitino mass formula accounting for CP violation and vacuum expectation values of current supermultiplet components in supergravity theories.

Findings

Induced gravitino mass when scalar or pseudoscalar currents acquire vacuum expectation values.

Generalization of supergravity action with cosmological constant to include CP violation.

Relation between vacuum energy, supersymmetry breaking, and gravitino mass.

Abstract

We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.