3D Gravity and Gauge Theories

Details 3D Gravity and Gauge Theories 3D Gravity and Gauge Theories

1993-11-16

arxiv.org/abs/hep-th/9311088v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pp., NBI-HE-93-67 (Contribution to Proceedings of 1993 Cargese workshop)

Scientific paper

I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes weighted with the Turaev-Viro invariant. Then, I discuss how this invariant can be included in the general framework of lattice gauge theory (qQCD$_3$). To make sense of it, one needs a quantum analog of the Peter-Weyl theorem and an invariant measure, which are introduced explicitly. The consideration here is limited to the simplest and most interesting case of $SL_q(2)$, $q=e^{i\frac{2\pi}{k+2}}$. At the end, I dwell on 3D generalizations of matrix models.

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