On deformations of AdS_n x S^n supercosets

Abstract

We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the "maximal" deformation limit kappa -> infinity this model is T-dual to "flipped" double Wick rotation of the target space AdS_5 x S^5, i.e. dS_5 x H^5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, kappa -> i, the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS_5 x S^5 superstring model. We also study in some detail similar deformations of the AdS_3 x S^3 and AdS_2 x S^2 supercosets. The bosonic part of the deformed AdS_3 x S^3 model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS_2 x S^2 case the role of the Fateev model is played by the 2d "sausage" model. The kappa = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS_n x S^n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS_3 x S^3 with more than one parameter.

31 pages; v2: 33 pages, comments on unitarity and finiteness added and misprints corrected; v3: minor changes

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• Integrability of classical strings dual for noncommutative gauge theories
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
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• Double Wick rotating Green-Schwarz strings
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• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
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• Analytic integrability for strings on $\eta$ and $\lambda$ deformed backgrounds
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Poisson-Lie duals of the eta deformed symmetric space sigma model
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
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• Spiky strings in $\varkappa$-deformed $AdS$
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Winding vacuum energies in a deformed O(4) sigma model
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
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• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Finite-size effect of η-deformed AdS_5 x S^5 at strong coupling
• Deformed WZW Models and Hodge Theory -- Part I
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Deformations of $T^{1,1}$ as Yang-Baxter sigma models
• Probing $\eta$ deformed backgrounds with $Dp$ branes
• Integrability structures in string theory
• NLIE for the Sausage model
• Field theory aspects of $\eta$-deformed superstring background
• Investigating (Non)-Integrability and Pulsating String in D3-Brane Background
• The sausage sigma model revisited
• Integrability and renormalizability for the fully anisotropic $\mathrm{SU}(2)$ principal chiral field and its deformations
• Asymptotics in the bi-Yang-Baxter Sigma Model
• Yang-Baxter deformations and string dualities
• Uniform Gauge for D1-brane in General Background
• Pulsating string solution and stability in two parameter $\chi$-deformed background