On Quantum Obstruction Spaces and Higher Codimension Gauge Theories

Abstract

Using the quantum construction of the BV-BFV method for perturbative gauge theories, we show that the obstruction for quantizing a codimension 1 theory is given by the second cohomology group with respect to the boundary BRST charge. Moreover, we give an idea for the algebraic construction of codimension $k$ quantizations in terms of ${\mathbb{E}}_k$-algebras and higher shifted Poisson structures by formulating a higher version of the quantum master equation.

arXiv comment18 pages, 4 figures, revised version for publication, typos fixed, to appear in Phys. Lett. B

References in corpus (35)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• Operads and Motives in Deformation Quantization
• A path integral approach to the Kontsevich quantization formula
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• Higher-dimensional Algebra and Topological Quantum Field Theory
• Geometry of Batalin-Vilkovisky quantization
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Another proof of M. Kontsevich formality theorem
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Deformations of algebras over operads and Deligne's conjecture
• Perturbative quantum gauge theories on manifolds with boundary
• Factorization homology of topological manifolds
• The tangent complex and Hochschild cohomology of E_n-rings
• Classical BV theories on manifolds with boundary
• Shifted Poisson Structures and Deformation Quantization
• On the origin of the BV operator on odd symplectic supermanifolds
• Derived coisotropic structures II: stacks and quantization
• A solution of Deligne's conjecture
• Derived coisotropic structures I: affine case
• Triviality of the higher Formality Theorem
• Braces and Poisson additivity
• Two-Dimensional Yang-Mills Theory on Surfaces With Corners in Batalin-Vilkovisky Formalism
• Split Chern-Simons theory in the BV-BFV formalism
• Introduction to the BV-BFV formalism
• Non-formality of the Swiss-Cheese operad
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• Kontsevich's Swiss Cheese Conjecture
• Introduction to Classical Gauge Field Theory and to Batalin-Vilkovisky Quantization
• Poisson reduction as a coisotropic intersection
• Donaldson Invariants and Their Generalizations from AKSZ Topological Field Theories
• Notes on Geometric Quantization
• On the generalization of the Darboux theorem
• Formality of a higher-codimensional Swiss-Cheese operad
• Weyl n-algebras and the Swiss cheese operad

Cited by in corpus (2)

• 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