On T-duality and integrability for strings on AdS backgrounds
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Publication:446679
DOI10.1088/1126-6708/2007/12/082zbMATH Open1246.81295arXiv0711.0707OpenAlexW2109827031MaRDI QIDQ446679
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Publication date: 8 September 2012
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/0711.0707
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