Perturbative BV theories with Segal-like gluing

TL;DR

This paper surveys a perturbative approach to quantizing gauge theories on manifolds with boundary, emphasizing compatibility with cutting and pasting, and illustrates the method with examples like abelian BF theory and the Poisson sigma model.

Contribution

It develops a framework for perturbative BV quantization of gauge theories with boundary, ensuring compatibility with geometric cutting and pasting operations.

Findings

Explicit quantization of abelian BF theory demonstrated

Quantization of the Poisson sigma model provided

Framework ensures gauge symmetry is maintained during cutting/pasting

Abstract

This is a survey of our program of perturbative quantization of gauge theories on manifolds with boundary compatible with cutting/pasting and with gauge symmetry treated by means of a cohomological resolution (Batalin-Vilkovisky) formalism. We also give two explicit quantum examples -- abelian BF theory and the Poisson sigma model. This exposition is based on a talk by P.M. at the ICMP 2015 in Santiago de Chile.