Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$

Abstract

We construct a family of type IIB string backgrounds that are deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$ with a "squashed" $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3$ metric supported by a combination of NSNS and RR fluxes. They have global $\mathrm{SU}(1,1)\times \mathrm{SU}(2)$ symmetry, regular curvature, constant dilaton and preserve 8 supercharges. Upon compactification to 4 dimensions they reduce to $\mathcal{N}=2$ supersymmetric $\mathrm{Ad}{\mathrm{S}}_2\times {\mathrm{S}}^2$ solutions with electric and magnetic Maxwell fluxes. These type IIB supergravity solutions can be found from the undeformed $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$ background by a combination of T-dualities and S-duality. In contrast to T-duality, S-duality transformations of a type IIB supergravity background do not generally preserve the classical integrability of the corresponding Green-Schwarz superstring sigma model. Nevertheless, we show that integrability is preserved in the present case. Indeed, we find that these backgrounds can be obtained, up to T-dualities, from an integrable inhomogeneous Yang-Baxter deformation (with unimodular Drinfel'd-Jimbo R-matrix) of the original $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3$ supercoset model.

arXiv comment34 pages, minor corrections

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