Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

TL;DR

This paper investigates the regularity of solutions in a supersymmetric nonlinear sigma model with gravitino fields, extending Dirac-harmonic maps and addressing analytic challenges with advanced mathematical techniques.

Contribution

It introduces a geometric framework for analyzing a supersymmetric sigma model with gravitino and explicitly derives its Euler-Lagrange equations, advancing understanding of its solutions' regularity.

Findings

Explicit Euler-Lagrange equations derived

Overcomes regularity challenges using Rivi e's theory

Establishes smoothness of weak solutions

Abstract

We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler--Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivi\`ere's regularity theory and Riesz potential theory.