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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.
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J. Balog, Á. Hegedűs, ”TBA equations for excited states in the O(3) and O(4) nonlinear σ \sigma -model”, J. Phys. A37 (2004) 1881, [arXiv:hep-th/0309009]
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2007
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G. Arutyunov and S. Frolov, “On String S-matrix, Bound States and TBA,” JHEP 0712
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2008
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A. Hegedus, F. Ravanini and J. Suzuki, “Exact finite size spectrum in super sine-Gordon model,” Nucl. Phys. B 763
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