On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism

Abstract

We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover, we consider mixed boundary conditions and show that they lead to quantum anomalies, i.e. to a failure of the (modified differential) Quantum Master Equation. We show that it can be restored by adding boundary terms to the action, at the price of introducing corner terms in the boundary operator. We also show that the quantum GBFV operator on the total space of states is a differential, i.e. squares to zero, which is necessary for a well-defined BV cohomology.

arXiv comment56 pages, 22 figures, glossary added, presentation improved for non experts. Section 2 is very similar to Section 2 of our companion paper arXiv:1807.11782. Also Appendix A.1-3, on the compactification of configuration spaces of manifolds with boundary, are taken from there but Section A.4, on the case of manifolds with corners, is added. To appear in Commun. Math. Phys

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• 4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism
• Computation of Kontsevich Weights of Connection and Curvature Graphs for Symplectic Poisson Structures
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
• Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theory
• Convolution algebras for Relational Groupoids and Reduction