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

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.

arXiv comment41 pages, 9 figures, typos fixed, presentation improved for non experts, to appear in Commun. Math. Phys

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Cited by in corpus (11)

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• General Relativity and the AKSZ construction
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• BV equivalence with boundary
• On Globalized Traces for the Poisson Sigma Model
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces
• 4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism
• Theta Invariants of lens spaces via the BV-BFV formalism
• Convolution algebras for Relational Groupoids and Reduction
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism