# Super-Symmetric Coupling: Existence and Multiplicity

## TL;DR

This paper introduces a method for analyzing critical points of indefinite energy functionals involving Dirac operators, with applications to Dirac-Geodesics and Yang-Mills-Dirac equations in two dimensions.

## Contribution

It develops a new approach to study strongly indefinite functionals coupled with fermionic Dirac operators, addressing existence and multiplicity of solutions.

## Key findings

- Established existence of solutions for Dirac-Geodesics problems.
- Analyzed the multiplicity of solutions in Yang-Mills-Dirac equations.
- Provided a framework applicable to energy functionals with fermionic coupling.

## Abstract

In this paper we provide a method to study critical points of strongly indefinite functionals on vector bundles. We focus mainly on energy functionals coupled with a fermionic part, that is with a Dirac-type operator. We consider the cases of the perturbed Dirac-Geodesics problem and the Yang-Mills-Dirac type equation in dimension two.