Chern-Simons Term for BF Theory and Gravity as a Generalized Topological Field Theory in Four Dimensions

Abstract

A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We first establish the generalized Chern-Weil homomormism for generalized curvature invariant polynomials in general even dimensional manifolds, and then show that BF gauge theory can be obtained from the action which is the generalized second Chern class with gauge group G. Particularly when G is taken as SL(2,C) in four dimensions, general relativity with cosmological constant can be derived by constraining the topological BF theory.

Improved abstract and introduction with 11 references added. Accepted for publication in Physical Review D

References in corpus (3)

• Large N Field Theories, String Theory and Gravity
• A holographic formulation of quantum general relativity
• Holographic Formulation of Quantum Supergravity

Cited by in corpus (10)

• (Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints
• Yang-Mills gravity in biconformal space
• Perturbative BF theory
• Higher Chern-Simons based on (2-)crossed modules
• Generalized forms and vector fields
• Topological gravity on plumbed V-cobordisms
• Effective Lagrangian for Non-Abelian Two-Dimensional Topological Field Theory
• Generalized forms and gravitation
• Generalized Chern-Simons action principles for gravity
• Generalized forms, vector fields and superspace