Renormalisation and the Batalin-Vilkovisky formalism

Abstract

This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renormalised in a way respecting all symmetries (up to homotopy). This yields an invariant of smooth manifolds: a certain algebraic structure on the cohomology of the manifold tensored with a Lie algebra, which is a "higher loop" enrichment of the natural Lie-infinity structure.

88 pages

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• The Geometry of the Master Equation and Topological Quantum Field Theory
• The BF Formalism for Yang-Mills Theory and the `t Hooft Algebra

Cited by in corpus (25)

• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Remarks on Chern-Simons invariants
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• BCOV theory via Givental group action on cohomological field theories
• Quantum $L_{\infty }$ Algebras and the Homological Perturbation Lemma
• Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
• Two-Dimensional Yang-Mills Theory on Surfaces With Corners in Batalin-Vilkovisky Formalism
• String Topology: Background and Present State
• Open Gromov-Witten theory on Calabi-Yau three-folds II
• Batalin-Vilkovisky Integrals in Finite Dimensions
• Unimodular homotopy algebras and Chern-Simons theory
• The geometry of variations in Batalin-Vilkovisky formalism
• BV quantization of the Rozansky-Witten model
• Operads and moduli spaces
• Quantum Yang-Mills Theory in Two Dimensions: Exact versus Perturbative
• Free frobenius algebra on the differential forms of a manifold
• Perturbative path-integral of string field and the $A_{\infty }$ structure of the BV master equation
• Master Equation and Perturbative Chern-Simons theory
• Factorization Algebras for Bulk-Boundary Systems
• Heat Kernel Renormalization on Manifolds with Boundary
• Differential operators and BV structures in noncommutative geometry
• The $L_{\infty }$-algebra of the S-matrix
• 2D and 3D topological field theories for generalized complex geometry
• On two constructions of an effective field theory