Liouville dressed weights and renormalization of spin in topologically massive gravity
Abstract
We examine the relations between observables in two and threedimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in nontrivial representations of the threedimensional Lorentz group. We show that the gravitational renormalization of spin up to oneloop order in these theories reproduces the leading orders of the KPZ scaling relations for quantum Liouville theory. We demonstrate that the twodimensional scaling dimensions can be computed from treelevel AharonovBohm scattering amplitudes between the charged particles in the limit where the threedimensional theory possesses local conformal invariance. We show how the threedimensional description defines scaledependent weights by computing the oneloop 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 threedimensional quantum gravity and argue that the topological ones may be related to the branched polymer phase of twodimensional quantum gravity.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)004665
 arXiv:
 arXiv:hepth/9703071
 Bibcode:
 1997NuPhB.502..383K
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 37 pages LaTeX