Conformal Dimensions from Topologically Massive Quantum Field Theory

TL;DR

This paper demonstrates how topologically massive quantum field theories can be used to compute conformal dimensions in two-dimensional conformal field theories through perturbative methods involving Aharonov-Bohm scattering amplitudes.

Contribution

It introduces a novel perturbative approach using topologically massive theories to derive conformal dimensions and explores their relation to quantum gravity effects.

Findings

One-loop corrections match scaling dimensions of WZNW models.

Aharonov-Bohm amplitudes relate to KPZ scaling in quantum gravity.

Perturbative techniques provide insights into 2D conformal field theories.

Abstract

We discuss the evaluation of observables in two-dimensional conformal field theory using the topological membrane description. We show that the spectrum of anomalous dimensions can be obtained perturbatively from the topologically massive quantum field theories by computing radiative corrections to Aharonov-Bohm scattering amplitudes for dynamical charged matter fields. The one-loop corrections in the case of topologically massive Yang-Mills theory are shown to coincide with the scaling dimensions of the induced ordinary and supersymmetric WZNW models. We examine the effects of the dressing of a topologically massive gauge theory by topologically massive gravity and show that the one-loop contributions to the Aharonov-Bohm amplitudes coincide with the leading orders of the KPZ scaling relations for two-dimensional quantum gravity. Some general features of the description of conformal field theories via perturbative techniques in the three-dimensional approach are also discussed.