Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

July 20, 2012

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

    (pdf, web)

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)(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: (k1)(k\!-\!1)-bundle gerbes) in each codimension kk.

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.

Posted at July 20, 2012 8:55 PM UTC

TrackBack URL for this Entry:

2 Comments & 0 Trackbacks

Re: Extended higher Chern-Simons theories

Typos on p. 2

…such that these assignmens…

The formal langauge…

Posted by: David Corfield on August 9, 2012 7:17 PM | Permalink | Reply to this

Re: Extended higher Chern-Simons theories

Typos on p. 2

Thanks for spotting these! I have fixed them now in our local copy. (These and other fixes will appear in the next arXiv version.)

Posted by: Urs Schreiber on August 12, 2012 5:18 PM | Permalink | Reply to this

Post a New Comment