Generalized $\lambda$-deformations of AdS_p x S^p

TL;DR

This paper explores the generalized lambda-deformation of string theories on AdS_p x S^p, providing explicit integrable backgrounds with preserved fluxes and analyzing the deformation's mathematical structure.

Contribution

It introduces a general form of the R-matrix for arbitrary cosets and shows that the deformation preserves the dilaton while modifying the frames by a constant matrix.

Findings

Explicit backgrounds for AdS_p x S^p with lambda-deformation

The dilaton remains unchanged under the deformation

The frames are multiplied by a constant matrix

Abstract

We study analytical properties of the generalized $\lambda$-deformation, which modifies string theories while preserving integrability, and construct the explicit backgrounds corresponding to AdS_p x S^p, including the Ramond-Ramond fluxes. For an arbitrary coset, we find the general form of the R-matrix underlying the deformation, and prove that the dilaton is not modified by the deformation, while the frames are multiplied by a constant matrix. Our explicit solutions describe families of integrable string theories depending on several continuous parameters.