Topological field theories in n-dimensional spacetimes and Cartan's equations

Abstract

Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first and second structure equations together with first and second Bianchi identities are treated as the equations of motion for a field theory. In opposition to that paper, the current approach involves also auxiliary fields and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis for the actions is detailedly carried out in the generic case and it is shown that these action principles define topological field theories, as mentioned. The current formalism is a generic framework to construct geometric theories with local degrees of freedom by introducing additional constraints on the various fields involved that destroy the topological character of the original theory. The latter idea is implemented in two-dimensional spacetimes where gravity coupled to matter fields is constructed out, which has indeed local excitations.

LaTeX file, no figures

References in corpus (7)

• The loop-quantum-gravity vertex-amplitude
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Covariant canonical formalism for four-dimensional BF theory
• Extended matter coupled to BF theory
• Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
• Two-dimensional topological field theories coupled to four-dimensional BF theory
• Genuine covariant description of Hamiltonian dynamics

Cited by in corpus (5)

• $BF$ gravity
• BF gravity with Immirzi parameter and cosmological constant
• Higher form Yang-Mills as higher BFYM theories
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• Towards a de Sitter quintom-like cosmology from a reduction of a 7-dimensional $BF$ theory