Fivebrane Structures

TL;DR

This paper explores the topological and cohomological aspects of fivebrane structures in string theory, linking anomaly cancellation conditions to higher geometric structures like String and Fivebrane structures.

Contribution

It introduces the concept of Fivebrane structures as higher analogs of String structures, connecting anomaly cancellation to obstructions in higher connected covers of structure groups.

Findings

Interpretation of one-loop terms via Pontrjagin classes

Definition of Fivebrane structures as higher lifts of structure groups

Relation between String and Fivebrane structures under duality

Abstract

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green-Schwarz anomaly cancelation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancelation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancelation points to a relation of String and Fivebrane structures under electric-magnetic duality.