$Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality

Abstract

We proceed to construct a dual pair for the $Ad{S}_3\times S^3$ background by applying non-Abelian T-duality (here as Poisson-Lie (PL) T-duality on a semi-Abelian double). By using a certain parametrization of the $4$-dimensional Lie group $A_2\otimes 2A_1$ and by a suitable choice of spectator-dependent matrices, the original $\sigma$-model including the $Ad{S}_3\times S^3$ metric and a non-trivial $B$-field are constructed. The dual background constructed by means of the PL T-duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non-trivial $H$-flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non-Abelian T-dual $\sigma$-models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two-loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.

24 pages

References in corpus (53)

• Double Field Theory
• Generalized metric formulation of double field theory
• Background independent action for double field theory
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Dual Non-Abelian Duality and the Drinfeld Double
• An Introduction to T-Duality in String Theory
• Integrability and the AdS(3)/CFT(2) correspondence
• On non-abelian T-dual geometries with Ramond fluxes
• Poisson-Lie T-duality
• On Nonabelian Duality
• On Non-Abelian Duality
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• Strings on Semisymmetric Superspaces
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Poisson-Lie T-Duality in Double Field Theory
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• Towards integrability for AdS3/CFT2
• AdS${}_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry
• Non-Abelian T-duality and consistent truncations in type-II supergravity
• Poisson-Lie T-plurality
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• The GS String Action on AdS(3)xS(3) with Ramond-Ramond Charge
• New $Ad{S}_3\times S^2$ T-duals with $\mathcal{N}=(0,4)$ supersymmetry
• The GS Type IIB Superstring Action on AdS(3) X S(3) X T(4)
• AdS${}_3$ solutions in massive IIA, defect CFTs and T-duality
• Poisson-Lie T-Duality: the Path-Integral Derivation
• Quantum Poisson-Lie T-duality and WZNW model
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Poisson-Lie T-Duality beyond the classical level and the renormalization group
• Poisson-Lie T-Duality and Supersymmetry
• Quantum correction to generalized T-dualities
• Poisson-Lie T-Duality and Bianchi Type Algebras
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Spinning strings in AdS_3 x S^3 with NS-NS flux
• ${\alpha }^{\prime }$-corrected Poisson-Lie T-duality
• Generalized Dualities and Higher Derivatives
• On the geometry of classically integrable two-dimensional non-linear sigma models
• Poisson-Lie T-dual sigma models on supermanifolds
• Classification of Poisson-Lie T-dual models with two-dimensional targets
• Poisson-Lie Duality in the String Effective Action
• BTZ black hole from Poisson-Lie T-dualizable sigma models with spectators
• Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group $H_4$
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach
• Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality
• T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality

Cited by in corpus (3)

• Classification of standard Manin triples in dimension 4+4
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations