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## $AdS_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations

### Abstract

Using the recently proposed set of discontinuity relations we translate the AdS/CFT Y-system to TBA integral equations and quantization conditions for a large subset of excited states from the sl(2) sector of the $AdS_5 \times S^5$ string sigma-model. Our derivation provides an analytic proof of the fact that the exact Bethe equations reduce to the Beisert-Staudacher equations in the asymptotic limit. We also construct the corresponding T-system and show that in the language of T-functions the energy formula reduces to a single term which depends on a single T-function.Comment: 67 pages, 4 figures; appendices added (published version

Topics: High Energy Physics - Theory
Year: 2012
DOI identifier: 10.1007/JHEP08(2011)095
OAI identifier: oai:arXiv.org:1104.4054