Spinor flows with flux, I: short-time existence and smoothing estimates

TL;DR

This paper introduces parabolic flows of spinor fields with flux, establishing short-time existence and smoothing estimates, which are relevant for supersymmetry in string theories and supergravity.

Contribution

It presents a new class of spinor flow equations with flux, analyzing their short-time existence and smoothing properties, advancing mathematical understanding of supersymmetric structures.

Findings

Established short-time existence of the flows.

Derived smoothing estimates for the spinor flows.

Identified stationary points as covariantly constant spinors.

Abstract

Spinor fields which are covariantly constant with respect to a connection with flux are of particular interest in unified string theories and supergravity theories, as their existence is required by supersymmetry. In this paper, flows of spinor fields are introduced which are parabolic and whose stationary points are such covariantly constant spinors.