Two-dimensional topological field theories coupled to four-dimensional BF theory

Abstract

Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two dimensional world-sheet. We show how two dimensional Yang-Mills degrees of freedom can be added on the world-sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world-sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background independent quantum field theory where local degrees of freedom at low energies arise from global topological (world-sheet) degrees of freedom at the fundamental level.

References in corpus (21)

• Background Independent Quantum Gravity: A Status Report
• Spin Foam Models for Quantum Gravity
• Relativistic spin networks and quantum gravity
• Spin Foam Models
• The loop-quantum-gravity vertex-amplitude
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Three dimensional loop quantum gravity: physical scalar product and spin foam models
• so(4) Plebanski Action and Relativistic Spin Foam Model
• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Classical Euclidean general relativity from ``left-handed area = right-handed area"
• BF gravity and the Immirzi parameter
• Three dimensional loop quantum gravity: coupling to point particles
• A spin foam model for pure gauge theory coupled to quantum gravity
• Covariant canonical formalism for four-dimensional BF theory
• Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double
• Feynman diagams coupled to three-dimensional quantum gravity
• Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
• Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory
• Feynman loops and three-dimensional quantum gravity
• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. II. Spin foam representation

Cited by in corpus (10)

• The Spin Foam Approach to Quantum Gravity
• An Invitation to Higher Gauge Theory
• $BF$ gravity
• Extended matter coupled to BF theory
• A pure Dirac's canonical analysis for four-dimensional BF theories
• Hamiltonian study for Chern-Simons and Pontryagin theories
• On gravitational defects, particles and strings
• Topological field theories in n-dimensional spacetimes and Cartan's equations
• The new spin foam models and quantum gravity
• Canonical Analysis of Algebraic String Actions