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Cellular BV-BFV-BF theory

Banff International Research Station for Mathematical Innovation and Discovery

We will present an example of a topological field theory living on cobordisms endowed with CW decomposition (this example corresponds to the so-called BF theory in its abelian and non-abelian variants), which satisfies the Batalin-Vilkovisky master equation, satisfies (a version of) Segal's gluing axiom w.r.t. concatenation of cobordisms and is compatible with cellularaggregations. In non-abelian case, the action functional of the theory is constructed out of local unimodular L-infinity algebras on cells; the partition function carries the information about the Reidemeister torsion, together with certain information pertaining to formal geometry of the moduli space of local systems. This theory provides an example of the BV-BFV programme for quantization of field theories on manifolds with boundary in cohomological formalism. This is a joint work with Alberto S. Cattaneo and Nicolai Reshetikhin.

Mathematics; Category theory; homological algebra; Quantum theory; Mathematical physics

video/mp4

Author affiliation: University of Notre Dame

2017-12-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63822

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/