Lectures on AKSZ Sigma Models for Physicists

TL;DR

This paper provides an introductory review of AKSZ sigma models, a class of topological field theories formulated using advanced mathematical structures, highlighting their construction, generalization, and quantization.

Contribution

It offers a comprehensive overview of the AKSZ construction, connecting topological field theories with supergeometry and gauge structures, and illustrates quantization through the Poisson sigma model.

Findings

Clarifies the AKSZ construction for TFTs

Generalizes to a broad class of sigma models

Demonstrates quantization with the Poisson sigma model

Abstract

This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional topological field theory and explain the ideas of the AKSZ sigma models. This construction is then generalized and leads to a mathematical formulation of a general topological sigma model. We review the mathematical objects, such as algebroids and supergeometry, that are used in the analysis of general gauge structures. The quantization of the Poisson sigma model is presented as an example of a quantization of an AKSZ sigma model.