*Extended higher Chern-Simons theories*

#### Posted by Urs Schreiber

We have been busy working on a little article. Now we feel it is time to show our current version around, before doing some last polishing and then posting it to the arXiv:

Domenico Fiorenza, Hisham Sati, Urs Schreiber,

*Extended higher cup-product Chern-Simons theories*

Check out section 1 *Introduction and overview*, for the story (6 pages). The rest is details.

I am grateful to the organizers of *String-Math 2012* for providing an environment in which this was finalized.

**Abstract.** It is well known that the proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors is given on gauge equivalence classes of higher gauge fields by the fiber integration of the cup product square of classes in degree-$(2k+2)$ differential cohomology.

We first refine this statement from gauge equivalence classes to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String-2-connections appearing in quantum-corrected 11-dimensional supergravity and on M-branes.

We discuss aspects of the off-shell extended geometric quantization (in the sense of extended or multi-tiered QFT) of these theories, with prequantum circle k-bundles (equivalently: $(k\!-\!1)$-bundle gerbes) in each codimension $k$.

Examples we include differential T-duality structures as well as the anomaly line bundles of higher electric/magnetic charges, such as the 5-brane charges appearing in heterotic supergravity, as line bundles with connection on the smooth higher moduli stacks field configurations.

## Re: Extended higher Chern-Simons theories

Typos on p. 2