On Fermion Masses, Gradient Flows and Potential in Supersymmetric Theories

TL;DR

This paper reviews general formulas in supergravity theories that relate fermion masses, scalar potentials, and symmetry breaking, emphasizing the roles of Killing vectors and prepotentials in N=1 and N=2 models.

Contribution

It provides a unified, model-independent framework for analyzing fermion masses and potentials in supergravity, with specific focus on quaternionic geometry in hypermultiplet dynamics.

Findings

Derived general relations for fermion masses and potentials.

Clarified the role of Killing vectors and prepotentials in symmetry breaking.

Discussed gauged quaternionic geometry in hypermultiplet sectors.

Abstract

In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played by Killing vectors and Killing prepotentials. We outline these relations in general and specify then in the context of N=1 and N=2 supergravities in four dimensions. Useful relations of gauged quaternionic geometry underlying hypermultiplets dynamics are discussed.