On T-Duality and Integrability for Strings on AdS Backgrounds

Abstract

We discuss an interplay between T-duality and integrability for certain classical non-linear sigma models. In particular, we consider strings on the AdS_5 x S^5 background and perform T-duality along the four isometry directions of AdS_5 in the Poincare patch. The T-dual of the AdS_5 sigma model is again a sigma model on an AdS_5 space. This classical T-duality relation was used in the recently uncovered connection between light-like Wilson loops and MHV gluon scattering amplitudes in the strong coupling limit of the AdS/CFT duality. We show that the explicit coordinate dependence along the T-duality directions of the associated Lax connection (flat current) can be eliminated by means of a field dependent gauge transformation. As a result, the gauge equivalent Lax connection can easily be T-dualized, i.e. written in terms of the dual set of isometric coordinates. The T-dual Lax connection can be used for the derivation of infinitely many conserved charges in the T-dual model. Our construction implies that local (Noether) charges of the original model are mapped to non-local charges of the T-dual model and vice versa.

20 pages; v2: misprints corrected, references and minor clarifications added

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• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• On (non)integrability of classical strings in p-brane backgrounds
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• Integrable 2d sigma models: quantum corrections to geometry from RG flow
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Duality between Wilson loops and gluon amplitudes
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
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• On the massless tree-level S-matrix in 2d sigma models
• On the geometry of classically integrable two-dimensional non-linear sigma models
• Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• Giant Magnon on Deformed AdS(3)xS(3)
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• A super MHV vertex expansion for N=4 SYM theory
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Integrable Superstrings on the Squashed Three-sphere
• Hidden Simplicity of Gauge Theory Amplitudes
• Spiky strings in $\varkappa$-deformed $AdS$
• On duality symmetry in perturbative quantum theory
• T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)
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• The Effective Action of N=8 Supergravity
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• $O(d,d)$ transformations preserve classical integrability
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• Integrability and duality in spin chains
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• Circular string in a Black p-brane leading to chaos
• Wilson loops T-dual to Short Strings
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• Peculiarities of String Theory on AdS(4) x CP(3)
• Stringy correlations on deformed $Ad{S}_3\times S^3$
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• Fermionic T-duality and U-duality in type II supergravity
• Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling
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• A Note on T-dualities in the Pure Spinor Heterotic String
• T-dualization of type II superstring theory in double space
• Fermionic T-duality and momenta noncommutativity
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Dirichlet boundary conditions in type IIB superstring theory and fermionic T-duality
• D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality
• Yangian symmetry of light-like Wilson loops
• Algebra of Lax Connection for T-Dual Models
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Note About String with Euclidean World-Sheet in AdS(5)xS(5)
• Integrated Lax Formalism for PCM