Conformal superspace sigma-models

TL;DR

This paper reviews recent advances in two-dimensional conformal sigma-models, emphasizing supergroup WZW models, their logarithmic conformal field theory structure, and dualities with other supersymmetric models.

Contribution

It provides a comprehensive overview of supergroup WZW models, their logarithmic structure, and explores marginal deformations and dualities in supersymmetric sigma-models.

Findings

Supergroup WZW models are key examples of logarithmic conformal field theories.

Exact anomalous dimensions can be computed using quasi-abelian perturbation theory.

A duality between the OSP(4|2) Gross-Neveu model and the S(3|2) supersphere sigma-model is proposed.

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.