On the AKSZ formulation of the Poisson sigma model

TL;DR

This paper reviews and extends the AKSZ construction for solutions of the BV classical master equation, focusing on sigma models with boundary, and relates the Poisson sigma model to deformation quantization and formality theorem.

Contribution

It provides an extended AKSZ framework for boundary sigma models, connecting the BV action of the Poisson sigma model to deformation quantization.

Findings

Derived BV action functional for Poisson sigma model on a disk

Linked perturbative quantization to Kontsevich's deformation quantization

Discussed diffeomorphism actions on target manifolds

Abstract

We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construction of solutions of the Batalin-Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin-Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.