Title: Classical and quantum Lagrangian field theories with boundaries I
Speaker: Alberto Cattaneo
Speaker Info: University of Zurich
Topological quantum field theories may be defined as appropriate functors from the cobordism category. The classical and perturbative versions thereof have started to be investigated only recently.Date: Thursday, March 29, 2012
We discuss topological field theories in the AKSZ formalism (this includes Chern-Simons and BF theories as well as the Poisson sigma model). In this case, to boundary components (objects) one can associate a symplectic manifold and a coisotropic submanifold, whereas to cobordisms one associates canonical relations. This very natural construction (a special case, but with more structure, of a more general one recently introduced by V. Fock), yields new viewpoints on, say, the moduli space of flat connections or the symplectic groupoid of a Poisson manifold. This also constitutes the starting point for the perturbative quantization of these theories. The possibility of including boundaries of boundaries (and so on) naturally yields to a Lurie-type description. Eventually, one may hope to be able to reconstruct perturbative topological field theories by gluing simple pieces.