Two-Dimensional Yang-Mills Theory on Surfaces With Corners in Batalin-Vilkovisky Formalism

Abstract

In this paper we recover the non-perturbative partition function of 2D~Yang-Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D~Yang-Mills theory on surfaces with boundaries and corners in the Batalin-Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting -- the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces -- building blocks -- and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D~Yang-Mills theory.

arXiv comment70 pages; small expository changes, citations added

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Cited by in corpus (16)

• Asymptotic symmetries in the BV-BFV formalism
• Towards holography in the BV-BFV setting
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• Fully extended BV-BFV description of General Relativity in three dimensions
• General Relativity and the AKSZ construction
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• Constrained systems, generalized Hamilton-Jacobi actions, and quantization
• BV equivalence with boundary
• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing
• 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
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
• Lattice defect networks in 2d Yang-Mills