p-Gerbes and Extended Objects in String Theory

TL;DR

This paper explores p-gerbes, a generalization of bundles with (p+2)-form field strengths, and demonstrates their role in describing p-dimensional extended objects and their classification via a K-theory framework.

Contribution

It develops the mathematical properties of p-gerbes and shows their equivalence to gauge theories with extended objects, introducing a K-theory for classifying their charges.

Findings

Every closed (p+2)-form with integer cohomology is a p-gerbe field strength.

p-Gerbes are equivalent to bundles with connection on p-submanifolds.

A K-theory of gerbes classifies charges of (p+1)-form connections.

Abstract

p-Gerbes are a generalization of bundles that have (p+2)-form field strengths. We develop their properties and use them to show that every theory of p-gerbes can be reinterpreted as a gauge theory containing p-dimensional extended objects. In particular, we show that every closed (p+2)-form with integer cohomology is the field strength for a gerbe, and that every p-gerbe is equivalent to a bundle with connection on the space of p-dimensional submanifolds of the original space. We also show that p-gerbes are equivalent to sheaves of (p-1)-gerbes, and use this to define a K-theory of gerbes. This K-theory classifies the charges of (p+1)-form connections in the same way that bundle K-theory classifies 1-form connections.