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

References in corpus (12)

• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
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• More supersymmetric Wilson loops
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• Strong-coupling expansion of cusp anomaly from quantum superstring
• Non-local charges, Zm gradings and coset space actions
• Perturbative study of the transfer matrix on the string worldsheet in AdS(5)xS(5)
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
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Cited by in corpus (10)

• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• T-duality in Ramond-Ramond backgrounds
• A super MHV vertex expansion for N=4 SYM theory
• The Effective Action of N=8 Supergravity
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Algebra of Lax Connection for T-Dual Models