Consistent 3D Quantum Gravity on Lens Spaces

Details Consistent 3D Quantum Gravity on Lens Spaces Consistent 3D Quantum Gravity on Lens Spaces

2011-09-05

arxiv.org/abs/1109.0793v2

Phys. Rev. D 85, 023520 (2012)

Physics

High Energy Physics

High Energy Physics - Theory

New section and references added. Accepted in Phys. Rev. D for publication

Scientific paper

We study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) on the background topology of lens space, which is a three spheres modulo a discrete group. Instead of the strategy followed by a recent work \cite{Castro:2011xb}, which compares results in the second and first order formulations of gravity, we concentrate on the later solely. We note, as a striking feature, that the quantization, that relies heavily on the axiomatics of topological quantum field theory (TQFT) can only be consistently carried by augmenting the conventional theory by an additional topological term coupled through a dimensionless parameter. More importantly the introduction of this additional parameter renders the theory finite.

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