On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets

TL;DR

This paper explores two integrable deformations of superstring sigma models on AdS_n x S^n supercosets, revealing their mathematical relationship and implications for supergravity backgrounds, with potential duality interpretations.

Contribution

It demonstrates that the eta-deformation can be derived from the lambda-deformation via a specific limit, establishing a connection between two integrable models of superstring theory.

Findings

The eta- and lambda-deformations are related through a scaling limit and analytic continuation.

The models correspond to different quantum deformation regimes (real and root of unity).

Evidence suggests they form a dual Poisson-Lie pair, especially in the S^2 case.

Abstract

We consider two integrable deformations of 2d sigma models on supercosets associated with AdS_n x S^n. The first, the "eta-deformation" (based on the Yang-Baxter sigma model), is a one-parameter generalization of the standard superstring action on AdS_n x S^n, while the second, the "lambda-deformation" (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the AdS_n x S^n superstring. We show that the eta-deformed model may be obtained from the lambda-deformed one by a special scaling limit and analytic continuation in coordinates combined with a particular identification of the parameters of the two models. The relation between the couplings and deformation parameters is consistent with the interpretation of the first model as a real quantum deformation and the second as a root of unity quantum deformation. For the AdS_2 x S^2 case we then explore the effect of this limit on the supergravity background associated to the lambda-deformed model. We also suggest that the two models may form a dual Poisson-Lie pair and provide direct evidence for this in the case of the integrable deformations of the coset associated with S^2.