Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism

TL;DR

This paper develops a global perturbative quantization framework for the Rozansky-Witten model within the BV-BFV formalism, extending the model to manifolds with boundary and ensuring consistency through quantum master equations.

Contribution

It introduces a globalization construction for the Rozansky-Witten model in the BV-BFV formalism, including a perturbative quantization and analysis of boundary operators.

Findings

Proves the modified differential Quantum Master Equation.

Establishes the flatness of the quantum Grothendieck BFV operator.

Constructs BFV boundary operators in specific cases.

Abstract

We describe a globalization construction for the Rozansky-Witten model in the BV-BFV formalism for a source manifold with and without boundary in the classical and quantum case. After having introduced the necessary background, we define an AKSZ sigma model, which, upon globalization through notions of formal geometry extended appropriately to our case, is shown to reduce to the Rozansky-Witten model. The relations with other relevant constructions in the literature are discussed. Moreover, we split the model as a $BF$-like theory and we construct a perturbative quantization of the model in the quantum BV-BFV framework. In this context, we are able to prove the modified differential Quantum Master Equation and the flatness of the quantum Grothendieck BFV operator. Additionally, we provide a construction of the BFV boundary operator in some cases.