Self-dual gravity with topological terms

Abstract

The canonical analysis of the (anti-) self-dual action for gravity supplemented with the (anti-) self-dual Pontrjagin term is carried out. The effect of the topological term is to add a `magnetic' term to the original momentum variable associated with the self-dual action leaving the Ashtekar connection unmodified. In the new variables, the Gauss constraint retains its form, while both vector and Hamiltonian constraints are modified. This shows, the contribution of the Euler and Pontrjagin terms is not the same as that coming from the term associated with the Barbero-Immirzi parameter, and thus the analogy between the theta-angle in Yang-Mills theory and the Barbero-Immirzi parameter of gravity is not appropriate.

LaTeX file, no figures, 8 pages. Accepted for publication in Class. Quantum Grav

Cited by in corpus (18)

• 4d Lorentzian Holst action with topological terms
• Actions, topological terms and boundaries in first order gravity: A review
• Hamiltonian and Noether charges in first order gravity
• A Immirzi-like parameter for 3d quantum gravity
• Covariant canonical formalism for four-dimensional BF theory
• Topological parameters in gravity
• Superconducting loop quantum gravity and the cosmological constant
• Quantum gravity as a Fermi liquid
• Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
• Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
• Noncommutative gravity with self-dual variables
• Hamiltonian dynamics of an exotic action for gravity in three dimensions
• The theta parameter in loop quantum gravity: effects on quantum geometry and black hole entropy
• On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries
• Anti Self-Dual Yang-Mills, Modified Faddeev-Jackiw Formalism and Hidden BRS Invariance
• Immirzi Ambiguity in the Kinematics of Quantum General Relativity
• Equivalence between various versions of the self-dual action of the Ashtekar formalism
• Gravity model from (A)dS Yang-Mills theory