### Dual Formulation of String Theory and Fivebrane Structures

#### Posted by Urs Schreiber

We would like to share the following:

Hisham Sati, U.S. and Jim Stasheff
*Dual Formulation of String Theory and Fivebrane Structures*

(pdf)
**Update**: now available as arXiv:0805.0564

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 cancellation condition can be read as a higher analog of String structure, which we callFivebrane 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.

This expands on some of the material announced in section 3 of

H. S., U.S., J. S.
*$L_\infty$-connections and application to String- and Chern-Simons transport*

(arXiv, blog pdf)

but so far concentrates on the topological aspects of Fivebrane structures. A discussion of the differential geometry of *Fivebrane 6-bundles* with connection – which are nonabelian differential cocycles that are to super 5-branes as String 2-bundles with connection are to superstrings and as ordinary Spin bundles with connection are to spinning particles – as well as of the Chern-Simons 7-bundles with connection obstructing their existence, will be given elsewhere, following the general approach described in

*On nonabelian differential cohomology*

(pdf).

I’d be grateful for comments, but should add that I’ll be travelling in Ireland until 3rd of May, which will reduce my responsiveness here for that period.

Posted at April 28, 2008 3:12 AM UTC
## Re: Dual Formulation of String Theory and Fivebrane Structures

Is this fivebrane really exactly like a string, but with 5 dimensions? What I mean is, with branes I heard that we get duals, but only for the classical version of the string or as soliton solutions formed by the endings of open branes.

So, is this really a higher dimensional dual with, with quantization, renomalizable, etc?