High spin limits and non-abelian T-duality

TL;DR

This work shows that non-abelian T-duals of WZW and PCM backgrounds arise as effective descriptions of sectors in a parent gauged sigma-model in the limit of diverging highest weights, with a correlated scaling of levels (e.g., $\ell = (k/\delta)\,j$) and spins ($j\to\infty$). Through explicit SU(2) examples, it demonstrates how scalar wave equations on dual backgrounds are recovered from high-spin limits of eigenstates constructed from group representations, and it extends the framework to non-isotropic and asymmetric cosets. The results illuminate the physical meaning of non-abelian T-duality as a sectoral, large-spin limit rather than a globally invertible map, and they point to deep links with integrable models and potential exact CFT descriptions. Overall, the paper provides a concrete, generalizable mechanism by which non-abelian T-duals emerge as effective backgrounds governing high-spin sectors of parent theories, with broad implications for non-abelian dualities in sigma-models.

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.