A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions

TL;DR

This paper proves a vanishing theorem for critical points of the supersymmetric nonlinear sigma model on certain non-compact manifolds with positive Ricci curvature, under specific geometric and energy conditions.

Contribution

It establishes a new vanishing result for supersymmetric sigma models in higher dimensions with positive Ricci curvature and Sobolev inequality assumptions.

Findings

Vanishing of critical points under small energy conditions

Applicable to complete non-compact manifolds with positive Ricci curvature

Extends understanding of supersymmetric sigma models in higher dimensions

Abstract

We prove a vanishing result for critical points of the supersymmetric nonlinear sigma model on complete non-compact Riemannian manifolds of positive Ricci curvature that admit an Euclidean type Sobolev inequality, assuming that the dimension of the domain is bigger than two and that a certain energy is sufficiently small.