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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 $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It takes the form of a $Y$ system based on the integrability of the dual superstring $\ensuremath{\sigma}$ model on the five-dimensional anti--de Sitter space (${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$) background. This …