Topological Higher Gauge Theory - from BF to BFCG theory

Abstract

We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature: the SigmaPhiEA-model of 3-dimensional gravity coupled to topological matter, and also a 4-dimensional model of BF-theory coupled to topological matter.

16 pages, LaTeX 2e with XYPic diagrams

References in corpus (9)

• Spherical Categories
• Diffeomorphisms and spin foam models
• Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics
• Higher gauge theory -- differential versus integral formulation
• State sum construction of two-dimensional open-closed Topological Quantum Field Theories
• 2-Groups, trialgebras and their Hopf categories of representations
• Loop Variables in Topological Gravity
• Scalar and tensorial topological matter coupled to (2+1)-dimensional gravity:A.Classical theory and global charges
• Higher Gauge Theory and Gravity in (2+1) Dimensions

Cited by in corpus (38)

• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• An Invitation to Higher Gauge Theory
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Higher lattices, discrete two-dimensional holonomy and topological phases in (3+1) D with higher gauge symmetry
• Topological phases from higher gauge symmetry in 3+1D
• Topological non-linear $\sigma$-model, higher gauge theory, and a realization of all 3+1D topological orders for boson systems
• Discrete gravity dynamics from effective spin foams
• Poincare 2-group and quantum gravity
• On $3$-gauge transformations, $3$-curvature and $\mathbf{Gray}$-categories
• Higher Gauge Theories Based on 3-groups
• Quantum geometry from higher gauge theory
• A 2-categorical state sum model
• Canonical formulation of Poincare BFCG theory and its quantization
• Hamiltonian analysis of the BFCG theory for the Poincare 2-group
• Topological invariant of 4-manifolds based on a 3-group
• Causal Dynamical Triangulations in the Spincube Model of Quantum Gravity
• Hamiltonian analysis of the BFCG formulation of General Relativity
• Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
• (2-)Drinfel'd Double and (2-)BF Theory
• Higher form Yang-Mills as higher BFYM theories
• Gauge symmetry of the 3BF theory for a generic Lie 3-group
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Discretization of 4d Poincaré BF theory: from groups to 2-groups
• Perturbative BF theory
• Higher Chern-Simons based on (2-)crossed modules
• Dynamical generalization of Yetter's model based on a crossed module of discrete groups
• Dynamics of a lattice 2-group gauge theory model
• Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• 3D Quantum Gravity from Holomorphic Blocks
• The 3BF theory as a TQFT
• Categorical generalization of spinfoam models
• Categorical generalization of BF theory coupled to gravity
• Adjusting Higher Chern-Simons Theory