Remarks on Non-Abelian Duality

TL;DR

The paper investigates 2D field theories that are globally scale-invariant but not conformally invariant, arising from non-Abelian duality based on non-semisimple isometry groups. By formulating A- and B-models and tracing the duality-induced non-local anomaly term (proportional to $\tfrac{1}{\Box}R^{(2)}$) that changes with the worldsheet curvature, it shows that if the original model is conformal, the dual can be made conformal after accounting for this anomaly; in flat backgrounds the spectra coincide. Through explicit examples, it demonstrates both how dual pairs can be reconciled by dilaton-type corrections and how a genuine scale-invariant, non-conformal dual can exist (e.g., in the GRV setup, with $c=4$). The work also develops mechanisms to localize the mixed anomaly by extending the target space or by bosonizing ghosts, providing a framework for understanding energy-momentum tensor relations and Ward identities across dual descriptions.

Abstract

A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality transformations, based on non-semisimple isometry groups. The construction of the dual partner of a given model is followed through; non-local as well as local versions of the former are discussed.