Exact Spectrum of Anomalous Dimensions of Planar<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-italic">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>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 sigma model on the five-dimensional anti-de Sitter space (AdS_{5} x S;{5}) 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 AdS_{4}/three-dimensional conformal field theory duality is also treated in a similar fashion.