Global Aspects of p-Branes

TL;DR

This paper extends the concept of string structures to higher-dimensional p-branes, analyzing their obstructions and quantization in the context of gauge fields and Wess-Zumino terms.

Contribution

It introduces a generalized notion of string structure for p-branes and explores their quantization and gauge transformation properties.

Findings

Constructed the quantization line bundle for p-branes.

Analyzed the action of background gauge transformations.

Discussed obstructions to extending string structures to p-branes.

Abstract

We generalize to dimension $p>1$ the notion of string structure and discuss the related obstruction. We apply our results to a model of bosonic $p$-branes propagating on a principal $G$-bundle, coupled to a Yang--Mills field and an antisymmetric tensor field and in the presence of a Wess-Zumino term in the Lagrangian. We construct the quantization line bundle and discuss the action of background gauge transformations on wave functions.