High spin limits and non-abelian T-duality

TL;DR

This paper explores the relationship between non-abelian T-duality and gauged WZW models, extending the equivalence to general sigma-models with non-abelian symmetries and illustrating it with examples.

Contribution

It generalizes the equivalence between non-abelian T-duals and gauged WZW models to a broader class of sigma-models, including Principal Chiral models.

Findings

Non-abelian T-duals correspond to states with large highest weight representations.

A limiting procedure relates non-abelian T-duals to effective backgrounds.

The method is demonstrated through several non-trivial examples.

Abstract

The action of the non-abelian T-dual of the WZW model is related to an appropriate gauged WZW action via a limiting procedure. We extend this type of equivalence to general sigma-models with non-abelian isometries and their non-abelian T-duals, focusing on Principal Chiral models. We reinforce and refine this equivalence by arguing that the non-abelian T-duals are the effective backgrounds describing states of an appropriate parent theory corresponding to divergently large highest weight representations. The proof involves carrying out a subtle limiting procedure in the group representations and relating them to appropriate limits in the corresponding backgrounds. We illustrate the general method by providing several non-trivial examples.