Bulk-boundary Correspondences via Factorization Algebras, II

A guiding example is due to Cattaneo and Felder, who showed how Kontsevich's deformation quantization of Poisson manifolds results from the quantization of a two-dimensional topological field theory on the upper half-plane. It is somewhat surprising that a two-dimensional field theory is used since a Poisson manifold encodes a classical mechanical system, i.e., a one-dimensional field theory. Cattaneo and Felder showed that there is a bulk-boundary correspondence between the two-dimensional theory and its boundary observables, the latter of which provide the desired deformation quantization. We will proffer a systematic generalization of this situation. First, we'll describe Poisson BV theories and bulk-boundary systems, and then relate the two via bulk-boundary correspondences. The general structure of these correspondences is that a Poisson BV theory can be understood to appear as a boundary condition of a bulk-boundary system. 

 

The first talk will illustrate the phenomena that occur for free Poisson BV theories and bulk-boundary systems. As a particular example, we note a correspondence between abelian Chern-Simons theory on the upper half-space and the chiral Kac-Moody algebra on the boundary plane. This is our joint work with Brian Williams. In this case, one can articulate both classical and quantum bulk-boundary correspondences.

 

In the second talk, we will discuss more recent work which generalizes these results to interacting classical Poisson BV theories.