Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces

Abstract

We consider a construction of observables by using methods of supersymmetric field theories. In particular, we give an extension of AKSZ-type observables using the Batalin-Vilkovisky structure of AKSZ theories to a formal global version with methods of formal geometry. We will consider the case where the AKSZ theory is "split" which will give an explicit construction for formal vector fields on base and fiber within the formal global action. Moreover, we consider the example of formal global generalized Wilson surface observables whose expectation values are invariants of higher-dimensional knots by using $BF$ field theory. These constructions give rise to interesting global gauge conditions such as the differential Quantum Master Equation and further extensions.

arXiv comment46 pages. slightly corrected version. discussion on L-infinity algebras and some references added

References in corpus (21)

• Deformation quantization of Poisson manifolds, I
• The Geometry of the Master Equation and Topological Quantum Field Theory
• A path integral approach to the Kontsevich quantization formula
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• Geometry of Batalin-Vilkovisky quantization
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Perturbative quantum gauge theories on manifolds with boundary
• Classical BV theories on manifolds with boundary
• On the Globalization of Kontsevich's Star Product and the Perturbative Poisson Sigma Model
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
• Remarks on Chern-Simons invariants
• Wilson surfaces and higher dimensional knot invariants
• On the origin of the BV operator on odd symplectic supermanifolds
• The Poisson sigma model on closed surfaces
• 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
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• Curved infinity-algebras and their characteristic classes

Cited by in corpus (3)

• 4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism
• BV Quantization
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism