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In this talk I will report on some precision test of the AdS/CFT
correspondence in the sector of scaling dimensions of local Wilson operators
in maximally supersymmetric Yang-Mills theory. After a brief introduction to
the Bethe ansatz approach to the spectral problem I will explain how to solve
the relevant equations in two limits of interest, the small and large spin limit.
I will then discuss the weak to strong coupling transition and demonstrate
the agreement with the string theory predictions at strong coupling.