Liouville dressed weights and renormalization of spin in topologically massive gravity

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 twodimensional quantum gravity.

Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory

“…Each term in the series yields string scattering amplitudes for a particular order g. The object one needs to compute to deal with the genus expansion is the partition function, or in other words the vacuum-to-vacuum amplitudes order by order, i.e. for each genus g. In this paper we will compute these objects using the topological membrane approach to string theory [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], which consists of replacing the string worldsheet by a three-dimensional manifold. Dynamically, it is modelled by a topologically massive gauge theory [36][37][38][39], i.e.…”

Open and unoriented Strings from topological membrane - I. Prolegomena

“…The projections P CT truncate the charge spectrum to q = m (due to demanding q = q) which corresponds in string theory to the KK momenta. Note that P CT excludes all the monopole induced processes while P T singles out only monopole induced processes [32,37,39].…”

“…The purpose of this work is to build open, open unoriented, and closed unoriented string theories (with and without orbifolding of the target space) from the Topological Membrane (TM) [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. This approach consists of a Topological Massive Gauge Theory (TMGT) [41][42][43] living on a 3D membrane, i.e.…”