Defining the AdS/CFT Y-system and Solving it Using a Finite Set of Equations

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I will show how to solve the AdS/CFT Y-system in terms of a finite set of nonlinear integral equations (FiNLIE). To uniquely define the solution we impose the set of constraints on the Y- and T-functions which can be summarized as: symmetry (PSU(2,2|4) + Z_4) + analyticity + large volume asymptotics. Some of these constraints describe previously unknown properties of the Y-system. As an important check of our approach, we showed that the proposed constraints can be also used to derive the infinite set of the TBA equations. We also successfully checked FiNLIE numerically for the case of Konishi operator.