Abstract
TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained is used to analyze the properties of Y-functions and address the issue of the existence of the critical values of the coupling. In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time.
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