Classical Bulk-Boundary Correspondences via Factorization Algebras

Abstract: A factorization algebra is a cosheaf-like local-to-global object which is meant to model the structure present in the observables of classical and quantum field theories. In the Batalin–Vilkovisky (BV) formalism, one finds that a factorization algebra of classical observables possesses, in addition to its factorization-algebraic structure, a compatible Poisson bracket of cohomological degree +1. Given a "sufficiently nice" such factorization algebra on a manifold $N$, one may associate to it a factorization algebra on $N\times \mathbb{R}_{\geq 0}$. The aim of the talk is to explain the sense in which the latter factorization algebra "knows all the classical data" of the former. This is the bulk-boundary correspondence of the title. Time permitting, we will describe how such a correspondence appears in the deformation quantization of Poisson manifolds.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Comments: Note unusual day and time.

Topological Quantum Field Theory Club (IST, Lisbon)

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