Quantum Gravity in 2+1 Dimensions

Abstract

General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting becomes an ideal test bed for a wide range of approaches to quantum gravity, from reduced phase phase space quantization to covariant canonical quantization to path integral methods to asymptotic quantization of "edge states." Here I review a variety of classical descriptions of the moduli space of solutions and a broad range of quantizations, with special attention to implications for realistic quantum gravity in four spacetime dimensions.

27 pages; invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics

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• Geometrical Foundations of Cartan Gauge Gravity
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• Complete loop quantization of a dimension 1+2 Lorentzian gravity theory
• Thermodynamical and dynamical stability of Einstein-Maxwell and extremal Einstein-Born-Infeld thin shells in $(2+1)$ dimensions
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation