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Topological limit of gravity admitting an SU(2) connection formulation

Journal Article · · Physical Review. D, Particles Fields
;  [1];  [1]
  1. Centre de Physique Theorique, Campus de Luminy, 13288 Marseille (France)

We study the Hamiltonian formulation of the generally covariant theory defined by the Lagrangian 4-form L=e{sub I} and e{sub J} and F{sup IJ}({omega}), where e{sup I} is a tetrad field and F{sup IJ} is the curvature of a Lorentz connection {omega}{sup IJ}. This theory can be thought of as the limit of the Holst action for gravity for the Newton constant G{yields}{infinity} and Immirzi parameter {gamma}{yields}0, while keeping the product G{gamma} fixed. This theory has for a long time been conjectured to be topological. We prove this statement both in the covariant phase space formulation as well as in the standard Dirac formulation. In the time gauge, the unconstrained phase space of theory admits an SU(2) connection formulation which makes it isomorphic to the unconstrained phase space of gravity in terms of Ashtekar-Barbero variables. Among possible physical applications, we argue that the quantization of this topological theory might shed new light on the nature of the degrees of freedom that are responsible for black entropy in loop quantum gravity.

OSTI ID:
21409415
Journal Information:
Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
Country of Publication:
United States
Language:
English