Supersymmetric field theories from twisted vector bundles

TL;DR

This paper connects the delocalized twisted cohomology of orbifolds and the Chern character of twisted vector bundles to supersymmetric Euclidean field theories, introducing a twist functor for 1|1-dimensional EFTs from gerbes with connection.

Contribution

It provides a new description of twisted cohomology and vector bundles using supersymmetric field theories, and constructs a twist functor for 1|1-dimensional EFTs from gerbes.

Findings

Describes delocalized twisted cohomology via supersymmetric field theories

Constructs a twist functor for 1|1-dimensional EFTs from gerbes with connection

Links geometric data with supersymmetric quantum field theories

Abstract

We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for $1|1$-dimensional EFTs from the data of a gerbe with connection.