# Y-system for the exact spectrum of AdS/CFT

*by V Kazakov*

*Institution:*Ecole Normale Superieure

*Date: Thu 19th August 2010*

*Time: 1:45 PM*

*Location: Room 910, Doug McDonnell Building, The University of Melbourne*

*Abstract*: Recently N.Gromov, P.Vieira and myself Â proposed the Y-system for exact spectrum of the Â AdS/CFT correspondence. We conjectured that it computes the spectrum of all anomalous dimensions in the four-dimensional planar N=4 super-Yang-Mills theory Â� at any value of the 'tHooft coupling constant. Â� Its AdS dual, the Â� superstring sigma-model on AdS5xS5 background, represents a remarkable case of two-dimentional non-relativistic Â� QFT exactly solvable by the standard 2D integrability

methods: asymptotic S-matrix and Bethe ansatz, as well as Â� TBA-like approach of Al.Zamolodchikov, allowing for the Â� derivation of the finite volume non-linear integral equations and their Y-system form. Solving this Y-system numerically we managed to compute the anomalous dimension of the shortest operator of the N=4 SYM theory - Konishi operator, at all couplings. I will describe recent successful checks of this Y-system, in the perturbation theory, where it reproduces analytically the known 4D Feynman graph expansion of SYM, at least up to 5 loops, and in the strong Â� coupling, where it also confirms the string theory predictions. The discrete integrable Hirota dynamics of this Y system will be discussed and its Wronskian determinant solution, recently found by N.Gromov,S.Leurent, Z.Tsuboi and myself, will be presented.

*For More Information:* contact: Iwan Jensen. email: I.Jensen@ms.unimelb.edu.au