# Gapped gravitinos, isospin $\frac{\mathbf{1}}{2}$ particles and $\mathcal{N}=2$ partial breaking

## TL;DR

This paper explores the topological properties of fermionic band structures in supersymmetric theories, revealing novel connections between partial supersymmetry breaking, fermionic gaps, and topological invariants.

## Contribution

It introduces a topological framework for analyzing partial supersymmetry breaking in 4D $
abla=2$ supergravity, linking fermionic gaps to chiral anomalies and supercurrent algebra.

## Key findings

- Identification of fermionic gapless modes via chiral anomaly
- Connection between spin-orbit coupling and supercurrent algebra
- Insights into discrete symmetries and quantum fluctuations in supersymmetric systems

## Abstract

Using results on topological band theory of phases of matter and discrete symmetries, we study topological properties of band structure of physical systems involving spin $\frac{1}{2}$ and $\frac{3}{2}$ fermions. We apply this approach to study partial breaking in 4D $\mathcal{N}=2$ gauged supergravity in rigid limit and we describe the fermionic gapless mode in terms of chiral anomaly. We study as well the homologue of the usual spin-orbit coupling $\vec{L}.\vec{S}$, that opens the vanishing band gap for free $s=\frac{1}{2}$ fermions; and show that is precisely given by the central extension of the $\mathcal{N}=2$ supercurrent algebra in 4D spacetime. We also give comments on the rigid limit of Andrianopoli et al obtained in [28] and propose an interpretation of energy bands in terms of a chiral gapless isospin $\frac{1}{2}$-particle (iso-particle). Other features, such as discrete T- symmetry in FI coupling space, effect of quantum fluctuations and the link with Nielson-Ninomiya theorem, are also studied.