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PIRSA:12050069

2+1 gravity as a conformal gauge theory and some frontiers for Shape Dynamics

APA

Gryb, S. (2012). 2+1 gravity as a conformal gauge theory and some frontiers for Shape Dynamics. Perimeter Institute for Theoretical Physics. https://pirsa.org/12050069

Sean Gryb University of Groningen

Talk numberPIRSA:12050069
Source RepositoryPIRSA
Talk Type Conference

Abstract

I will start by showing that gravity, with positive cosmological constant in 2+1 dimensions, can be formulated as a theory of dynamic conformal spatial geometry. Exploiting the isomorphism between the isometry group of de Sitter space in D+1 dimensions and the conformal group in D dimensions, I will reinterpret the Chern--Simons formulation of 2+1 gravity as a gauge theory of a conformal connection. In Cartan's generalization of geometry, this connection represents an evolving spatial geometry locally modeled off the conformal sphere. After a suitable phase space reduction, we obtain shape dynamics. This remodeling explains, in 2+1 dimensions, the remarkable success of the York procedure for solving the initial value problem of general relativity and the uniqueness of the shape dynamics Hamiltonian. I will finish by speculating about possible connections between this work and the general shape dynamics program with holographic renormalization, AdS/CFT, and Horava gravity.