Conformal superspace σ-models

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Review

Mitev, Vladimir²  Quella, Thomas¹  Schomerus, Volker² 

[1] Univ Amsterdam, Korteweg de Vries Inst Math, NL-1090 GE Amsterdam, Netherlands

[2] DESY Hamburg, Theory Grp, D-22607 Hamburg, Germany

关键词: Conformal field theory;    Supergeometry;    Harmonic analysis;   

DOI  :  10.1016/j.geomphys.2010.11.004

来源: Elsevier

【 摘 要 】

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 vertical bar 2) symmetric Gross-Neveu model and the S-3 vertical bar 2 supersphere sigma-model. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free