Wednesday, April 9, 2003, 1:00pm, 277 Phillips Hall, String Theory Seminar
James Stasheff (University of North Carolina),
Poisson sigma models, Batalin-Vilkovisky machinery and Linfinity-algebra
Kontsevich's formal proof that deformation quantization is possible for any Poisson manifold made crucial use of Linfinity-algebras. Cattaneo and Felder gave a `stringy' proof in terms of Feynman `path' integrals after applying the Batalin-Vilkovisky machinery. The Linfinity-algebra structure is there but hidden in their proof. The talk will start with the Cattaneo-Felder Lagrangian involving the fields of a Poisson sigma model. After reviewing the Batalin-Vilkovisky machinery of anti-fields, ghosts and anti-ghosts, it will be applied to the C-F model and then reformulated in their `super' setting. Linfinity-algebra will be defined and illustrated in this context. The relation to the `field dependent' symmetries of Behrens, Burgers and van Dam will be explained.