Five-brane Instantons vs Flux-induced Gauging of Isometries

TL;DR

This paper explores how background flux in five-dimensional heterotic M-theory constrains M5-brane instantons to preserve certain isometries, analyzing zero modes via Dirac equations under flux conditions.

Contribution

It demonstrates that flux backgrounds restrict M5-brane instantons to those preserving specific isometries, extending string theory insights to M-theory and analyzing zero modes with fluxes.

Findings

Flux allows only isometry-preserving instantons

Zero-mode solutions relate to Dirac equation on instanton worldvolume

Analysis includes generic and nonzero worldvolume flux cases

Abstract

In five-dimensional heterotic M-theory there is necessarily nonzero background flux, which leads to gauging of an isometry of the universal hypermultiplet moduli space. This isometry, however, is poised to be broken by M5-brane instanton effects. We show that, similarly to string theory, the background flux allows only brane instantons that preserve the above isometry. The zero-mode counting for the M5 instantons is related to the number of solutions of the Dirac equation on their worldvolume. We investigate that equation in the presence of generic background flux and also, in a particular case, with nonzero worldvolume flux.