Integrable supersymmetric deformations of AdS3 × S3 × T4

Abstract

We construct a family of type IIB string backgrounds that are deformations of AdS3× S3× T4 with a “squashed” AdS3× S3 metric supported by a combination of NSNS and RR fluxes. They have global SU(1, 1) × SU(2) symmetry, regular curvature, constant dilaton and preserve 8 supercharges. Upon compactification to 4 dimensions they reduce to $$ \mathcal{N} $$ N = 2 supersymmetric AdS2× S2 solutions with electric and magnetic Maxwell fluxes. These type IIB supergravity solutions can be found from the undeformed AdS3× S3× T4 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 AdS3× S3 supercoset model.

Supersymmetric backgrounds from λ-deformations

“…The closest in spirit to our present work is the supersymmetric deformation of the AdS3 × S 3 × T 4 solution studied in [31]. This deformation also preserves one-quarter of the maximal supersymmetry and can be found by applying TsT transformations to the one-parameter Yang-Baxter integrable deformation [22][23][24].…”

Elliptic deformations of the AdS3 × S3 × T4 string

“…an integrable trigonometric deformation of strings on AdS 3 × S 3 × T 4 was constructed in [13,14]. Motivated by these results, our goal in this paper is to investigate the existence of an integrable elliptic deformation of strings on AdS 3 × S 3 × T 4 .…”

“…3 In particular, when only one factor is deformed, which we refer to as a unilateral deformation, then at least half the supersymmetry will be preserved. Moreover, for the unilateral inhomogeneous YB deformation constructed from the Drinfel'd-Jimbo R-matrix, the resulting geometry is smooth with vanishing Ricci scalar and the dilaton is constant [13,14].…”

“…The deformed bosonic sigma models are the same up to a total derivative. While the YB deformation leads a particular choice of supporting R-R fluxes, by applying sequences of TsT transformations in the 4-torus directions it is possible to write the background in an SO(4)-invariant way [14], where SO( 4) is locally isomorphic to the maximal compact subgroup of the T-duality group of 6-d maximal supergravity. 4 We refer to this model as the trigonometric deformation of strings on AdS 3 × S 3 × T 4 .…”

“…4 This can be extended to include the Neveu-Schwarz-Neveu-Schwarz (NS-NS) 3-form flux starting from the unilateral inhomogeneous Drinfel'd-Jimbo bi-YB deformation [15] of the AdS3 × S 3 mixed flux supercoset sigma model [16]. Again by applying sequences of TsT transformations, the background can be written in an SO(5)-invariant way [14], where SO( 5) is locally isomorphic to the maximal compact subgroup of the U-duality group of 6-d maximal supergravity.…”