Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary

TL;DR

This paper develops a covariant, globalized framework for perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with boundary, incorporating formal geometry to understand quantum state changes.

Contribution

It introduces a globalized quantization approach using formal geometry, extending the BV-BFV formalism with a modified differential Quantum Master Equation.

Findings

Constructs a covariant globalized quantization framework.

Shows quantum states as closed sections under a zero-square operator.

Generalizes the Quantum Master Equation in the BV-BFV formalism.

Abstract

We describe a covariant framework to construct a globalized version for the perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with and without boundary, and show that it captures the change of the quantum state as one changes the constant map around which one perturbs. This is done by using concepts of formal geometry. Moreover, we show that the globalized quantum state can be interpreted as a closed section with respect to an operator that squares to zero. This condition is a generalization of the modified Quantum Master Equation as in the BV-BFV formalism, which we call the modified "differential" Quantum Master Equation.