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arXiv · hep-th/9703071

Liouville Dressed Weights and Renormalization of Spin in Topologically Massive Gravity

Ian I. Kogan·Richard J. Szabo
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Abstract

We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We show that the gravitational renormalization of spin up to one-loop order in these theories reproduces the leading orders of the KPZ scaling relations for quantum Liouville theory. We demonstrate that the two-dimensional scaling dimensions can be computed from tree-level Aharonov-Bohm scattering amplitudes between the charged particles in the limit where the three-dimensional theory possesses local conformal invariance. We show how the three-dimensional description defines scale-dependent weights by computing the one-loop order anomalous magnetic moment of fermions in a background electromagnetic field due to the renormalization by topologically massive gravity. We also discuss some aspects concerning the different phases of three-dimensional quantum gravity and argue that the topological ones may be related to the branched polymer phase of two-dimensional quantum gravity.

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Ian I. Kogan, Richard J. Szabo. 1997-03-10. Liouville Dressed Weights and Renormalization of Spin in Topologically Massive Gravity. https://doi.org/10.1016/s0550-3213(97)00466-5

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