Dual Formulation of String Theory and Fivebrane Structures

We would like to share the following:

Hisham Sati, U.S. and Jim Stasheff

Dual Formulation of String Theory and Fivebrane Structures

(pdf)

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 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.

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

H. S., U.S., J. S.

$L_{\mathrm{\infty }}$-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.