Topological BF Theories in 3 and 4 Dimensions

Abstract

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide range of invariants. Here we consider mainly the 3-dimensional case, where these invariants include Alexander polynomials, HOMFLY polynomials and Kontsevich integrals.

25 pages, latex, no figures. Transmission problems have been solved

Cited by in corpus (64)

• Non-Abelian Anyons and Topological Quantum Computation
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• Hamiltonian Analysis of Plebanski Theory
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
• Configuration spaces and Vassiliev classes in any dimension
• Kontsevich Integral for Vassiliev Invariants from Chern-Simons Perturbation Theory in the Light-Cone Gauge
• $BF$ gravity
• Tensor Berry connections and their topological invariants
• Finite Type Invariants of w-Knotted Objects I: w-Knots and the Alexander Polynomial
• Feynman rules and beta-function for the BF Yang-Mills Theory
• Three-dimensional de Sitter horizon thermodynamics
• The century of the incomplete revolution: searching for general relativistic quantum field theory
• The BF Formalism for QCD and Quark Confinement
• On the Relations between Gravity and BF Theories
• A Immirzi-like parameter for 3d quantum gravity
• Loop Quantum Gravity a la Aharonov-Bohm
• A new Hamiltonian for the Topological BF phase with spinor networks
• Causality and matter propagation in 3d spin foam quantum gravity
• An Exotic Theory of Massless Spin-Two Fields in Three Dimensions
• Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables
• (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
• Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds
• Towards holography in the BV-BFV setting
• BF-theory in graphene: a route toward topological quantum computing?
• Quantum Theory of Large Systems of Non-Relativistic Matter
• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• Cabled Wilson Loops in BF Theories
• Abelian BF theory and Turaev-Viro invariant
• Topological Features of the Quantum Vacuum
• Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne
• Combinatorial Formulae for Vassiliev Invariants from Chern-Simons Gauge Theory
• 4-dimensional BF Gravity on the Lattice
• One-dimensional Chern-Simons theory
• (Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• The geometry of graded cotangent bundles
• Supergravity as a constrained BF theory
• Canonical Structure of Field Theories with Boundaries and Applications to Gauge Theories
• Abelian BF Theories and Knot Invariants
• Chiral Symmetry and the Cosmological Constant
• Higher form Yang-Mills as higher BFYM theories
• Gauge-Invariant Operators for Singular Knots in Chern-Simons Gauge Theory
• Anomalies and Renormalization of BFYM Theory
• Perturbative BF theory
• Loop observables for BF theories in any dimension and the cohomology of knots
• From simplicial Chern-Simons theory to the shadow invariant I
• From simplicial Chern-Simons theory to the shadow invariant II
• Dimension of the moduli space and Hamiltonian analysis of BF field theories
• On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants
• Black hole and cosmological analysis of BF sequestered gravity
• Covariant momentum map for non-Abelian topological BF field theory
• Ruelle zeta function from field theory
• Effective Lagrangian for Non-Abelian Two-Dimensional Topological Field Theory
• BRST Symmetries for the Tangent Gauge Group
• Mass generation from a non-perturbative correction: Massive NS-field and graviton in $(3+1)$-dimensions
• Cosmological Plebanski theory
• The van Est homomorphism for strict Lie 2-groups
• Spin current in BF theory
• The dynamics on the three-dimensional boundary of the 4D Topological BF model
• Discrete canonical analysis of three dimensional gravity with cosmological constant
• Hessian in the spinfoam models with cosmological constant
• Perturbative BF theory in axial, Anosov, gauge