Maths HEP Lunchtime Seminars: Quantum Field Theory on Non-Abelian Gerbes
20 January 2006 13:00 in CM221
"The natural generalisation of a principal bundle is a non-Abelian gerbe. The differential geometry of these objects is known since the work of Breen and Messing. I will discuss this structure in a way which allows for a direct path-integral quantisation as a Quantum Field Theory. This involves, in particular, introducing (locally) the notion of the Universal Gerbe, constructing an identically nilpotent BRST operator as a differential on it, and imposing a certain constraint algebra in the cohomology of that operator. As an example I will describe global configurations of the maximally supersymmetric Yang-Mills theory in four dimensions that have the structure of a cohomologically non-trivial non-Abelian gerbe. The cohomology class of the gerbe can be interpreted as a generalisation of 't Hooft's magnetic flux."