“Batalin-Vilkovisky formalism in topological quantum field theory”

Schedule: Mondays 10-12; first lecture on 06.10.2014
Where: MATH/SemR 0.008, Endenicher Allee 60

(Tentative) course program

- Examples of gauge theories: Yang-Mills, Chern-Simons, BF, Poisson sigma model,...

- Faddeev-Popov construction (a supergeometric resolution of integrals over quotients by group actions).

- BRST formalism, cohomological vector fields.

- Batalin-Vilkovisky formalism: odd symplectic geometry, the master equation. Integration theory on supermanifolds; BV integrals and BV pushforwards (effective actions). Relation to infinity-algebras and homotopy transfer.

- AKSZ construction of solutions of the master equation on mapping spaces between Q-manifolds. Examples. AKSZ moduli spaces.

- Kontsevich's deformation quantization via Poisson sigma model.

- Perturbative Chern-Simons theory via BV formalism. Hodge-de Rham gauge-fixing and “soft” propagators. Toy model associated to differential graded Frobenius algebras. Configuration space integrals and knot invariants.

- Cellular BF theory on simplicial/cubical/prismatic complexes. R-torsion via BV pushforward.

- Extension of BV formalism to spacetime manifolds with boundary, consistent with Atiyah-Segal gluing.