Conformal dimensions from topologically massive quantum field theory

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.

Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theory

“…At a generic point of the moduli space M, the gauge group G is spontaneously broken by the holonomies to the Abelian subgroup V. Some components of the spinor field are then massive and can be integrated out. This procedure is responsible for the shift of the Chern-Simons level from k to k 0 ¼ k À h=2 as mentioned in the introduction [2,3]. We denote the remaining fermionic degrees of freedom, which consist of spatially constant V-valued modes, as þ and À .…”

“…This is best expressed in terms of a shifted level [2,3] k 0 ¼ k À h=2; (1.6) where h is the dual Coxeter number of G. For a simply connected gauge group…”

Strings, Gauge Fields and Membranes

“…The natural identifications of the two models can now be heuristically deduced from the group isomorphism 8) inducing both chiralities of the SL(2, R) worldsheet theory as in (5.6). The gravitational dressing of conformal field theories by topologically massive gravity is studied in [49,50]. In addition to inducing the gravitational sector of the string theory, we see from (5.6) that the scalar field D can be naturally identified as the three-dimensional version of the string dilaton field.…”

Vacuum instability in topologically massive gauge theory

“…Of course, in the supersymmetric models we have to shift k → k − C 2 compared to the bosonic models [11,15,12], but clearly this cannot be seen at this order. Also, we would not expect a critical charge at ψ · µ = k/2 as this representation is included in the physical spectrum of the WZNW model, and we would expect a critical charge to be screened a particle-antiparticle pair which could condense from the vacuum.…”