3D Gravity and Gauge Theories

D. V. Boulatov

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arXiv · hep-th/9311088

3D Gravity and Gauge Theories

D. V. Boulatov

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Abstract

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 $SL_q(2)$, $q=e^{i\frac{2π}{k+2}}$. At the end, I dwell on 3D generalizations of matrix models.

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D. V. Boulatov. 1993-11-16. 3D Gravity and Gauge Theories. https://arxiv.org/abs/hep-th/9311088

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