Remarks on Chern-Simons invariants

Abstract

The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.

33 pages; minor corrections, new appendices with technical details, new references, new example; to appear in Commun. Math. Phys.

References in corpus (4)

• Renormalisation and the Batalin-Vilkovisky formalism
• Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
• Master Equation and Perturbative Chern-Simons theory
• Discrete BF theory

Cited by in corpus (34)

• Perturbative quantum gauge theories on manifolds with boundary
• Classical BV theories on manifolds with boundary
• Double Copy from Homotopy Algebras
• Loop Amplitudes and Quantum Homotopy Algebras
• The Poisson sigma model on closed surfaces
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• Split Chern-Simons theory in the BV-BFV formalism
• A model for configuration spaces of points
• Finite dimensional AKSZ-BV theories
• A cellular topological field theory
• Semiclassical quantization of classical field theories
• Equivariant Rozansky-Witten classes and TFTs
• Unimodular homotopy algebras and Chern-Simons theory
• The Lambrechts-Stanley Model of Configuration Spaces
• One-dimensional Chern-Simons theory
• Constrained systems, generalized Hamilton-Jacobi actions, and quantization
• BV quantization of the Rozansky-Witten model
• Minimal models of quantum homotopy Lie algebras via the BV-formalism
• Operads and moduli spaces
• Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor
• Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
• Quantum Yang-Mills Theory in Two Dimensions: Exact versus Perturbative
• Batalin-Vilkovisky quantization of fuzzy field theories
• Master Equation and Perturbative Chern-Simons theory
• Twisted IBL-infinity-algebra and string topology: First look and examples
• Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces
• IBL-Infinity Model of String Topology from Perturbative Chern-Simons Theory
• 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
• BV Quantization
• Lecture Notes on Chern-Simons Perturbation Theory
• A holography theory of Poisson sigma model and deformation quantization
• Lagrangian Relations and Quantum $L_{\infty }$ Algebras
• Hodge decompositions and Poincare duality models