CONFORMAL DIMENSIONS FROM TOPOLOGICALLY MASSIVE QUANTUM-FIELD THEORY

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 fr om the topologically massive quantum field theories by computing radia tive corrections to Aharonov-Bohm scattering amplitudes for dynamical charged matter fields, The one-loop corrections in the case of topolog ically massive Yang-Mills theory are shown to coincide with the scalin g dimensions of the induced ordinary and supersymmetric WZNW models, W e examine the effects of the dressing of a topologically massive gauge theory by topologically massive gravity and show that the one-loop co ntributions to the Aharonov-Bohm amplitudes coincide with the leading orders of the KPZ scaling relations for two-dimensional quantum gravit y. Some general features of the description of conformal field theorie s via perturbative techniques in the three-dimensional approach are al so discussed.