On Globalized Traces for the Poisson Sigma Model

TL;DR

This paper develops a globalized trace formula for the Poisson Sigma Model using the Batalin-Vilkovisky formalism, connecting it to symplectic geometry and established theorems in deformation quantization.

Contribution

It introduces a globalized trace construction for the Poisson Sigma Model, incorporating zero modes and linking to key theorems in deformation quantization.

Findings

Globalized trace formula for Poisson Sigma Model on the disk.

Reduction to a symplectic construction in the cotangent target case.

Connection to Nest-Tsygan and Tamarkin-Tsygan theorems.

Abstract

A globalized version of a trace formula for the Poisson Sigma Model on the disk is presented by using its formal global picture in the setting of the Batalin-Vilkovisky formalism. This global construction includes the concept of zero modes. Moreover, for the symplectic case of the Poisson Sigma Model with cotangent target, the globalized trace reduces to a symplectic construction which was presented by Grady, Li and Li for 1-dimensional Chern-Simons theory (topological quantum mechanics). In addition, the connection between this formula and the Nest-Tsygan theorem and the Tamarkin-Tsygan theorem is explained.