Conformal superspace sigma-models
Abstract
We review recent developments in the context of two-dimensional conformally invariant sigma-models. These quantum field theories play a prominent role in the covariant superstring quantization in flux backgrounds and in the analysis of disordered systems. We present supergroup WZW models as primary examples of logarithmic conformal field theories, whose structure is almost entirely determined by the underlying supergeometry. In particular, we discuss the harmonic analysis on supergroups and supercosets and point out the subtleties of Lie superalgebra representation theory that are responsible for the emergence of logarithmic representations. Furthermore, special types of marginal deformations of supergroup WZW models are studied which only exist if the Killing form is vanishing. We show how exact expressions for anomalous dimensions of boundary fields can be derived using quasi-abelian perturbation theory. Finally, the knowledge of the exact spectrum is used to motivate a duality between the OSP(4|2) symmetric Gross-Neveu model and the S(3|2) supersphere sigma-model.
Cite
@article{arxiv.1210.8159,
title = {Conformal superspace sigma-models},
author = {Vladimir Mitev and Thomas Quella and Volker Schomerus},
journal= {arXiv preprint arXiv:1210.8159},
year = {2012}
}
Comments
21 Pages, 7 Figures, 2 Tables. Based on a talk given by Thomas Quella at the Lorentz Center Workshop "The Interface of Integrability and Quantization" (Leiden, 12.-16.4.2010). Version close to that published in Journal of Geometry and Physics