Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory

We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 supersymmetric Yang-Mills theory. It takes the form of a Y system based on the integrability of the dual superstring σ model on the five-dimensional anti–de Sitter space (AdS₅×S⁵) background. This Y system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS₄/three-dimensional conformal field theory duality is also treated in a similar fashion.