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.

34 pages, minor corrections

References in corpus (23)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Quantum Deformations of the One-Dimensional Hubbard Model
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Towards integrability for AdS3/CFT2
• A Jordanian deformation of AdS space in type IIB supergravity
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Yangian symmetry in deformed WZNW models on squashed spheres
• Integrable Deformations of Sigma Models
• Schrödinger geometries arising from Yang-Baxter deformations
• Hidden Yangian symmetry in sigma model on squashed sphere
• Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Warped anti-de Sitter spaces from brane intersections in type II string theory
• Unimodular jordanian deformations of integrable superstrings
• Conformal Symmetries for Extremal Black Holes with General Asymptotic Scalars in STU Supergravity
• Integrable deformations of AdS/CFT
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Bethe Ansatz for Quantum-Deformed Strings

Cited by in corpus (6)

• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Supersymmetric backgrounds from $\lambda$-deformations
• Supersymmetric solutions of type-II supergravity from $\lambda$-deformations and zoom-in limits
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Type-II backgrounds from deformed coset CFTs
• Pulsating string solution and stability in two parameter $\chi$-deformed background