Topological Field Theory (Part One)
David Ben-Zvi (The University of Texas at Austin)
April 13th, 2007 at University of Oxford
Special thanks to Charles Beesley, Head of Media Production, University of Oxford
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Abstract:
An exciting recent development is the emergence of a profound connection between the geometric Langlands program and topological quantum field theories, due to Kapustin and Witten. In their approach, the geometric Langlands duality is described as a two-dimensional manifestation of the electric-magnetic duality of supersymmetric four-dimensional gauge theories. Starting from the axiomatic definition of topological field theories we will see the basic structures of geometric Langlands emerge. The finer features come out of detailed examination of observables in gauge theories, mirror symmetry for hyperk"ahler manifolds and the categories of boundary conditions (D-branes).