On Fermion Masses, Gradient Flows and Potential in Supersymmetric Theories

TL;DR

This work derives model-independent relations linking fermion masses, gradient flows, and scalar potentials in 4D N=1 and N=2 supergravity through geometric data such as Killing vectors and prepotentials. By analyzing SUSY variations, the authors express the scalar potential and fermionic mass matrices entirely in terms of fermion shifts and their gradient flows, with special attention to the interplay between special Kähler and quaternionic (or dual quaternionic) geometries under gauging. In N=2, the results reveal how gradient-flow structures arise from the coupled vector and hypermultiplet geometries and provide criteria for preserving supersymmetry, including the role of P^x_Λ and k^i in determining AdS vacua and BPS configurations. The paper further discusses dual quaternionic manifolds, the c-map, and universal gaugings, showing how gauging solvable symmetry algebras governs the low-energy effective dynamics in Calabi–Yau compactifications and related string/M-theory settings.

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.