Abstract
We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. From this, we numerically evaluate the nonplanar contribution to the four-loop lightlike cusp anomalous dimension and derive the transcendental ζ_{3} and ζ_{5} parts of the universal anomalous dimension for arbitrary Lorentz spin in analytic form. As for the lightlike cusp anomalous dimension and the ζ_{5} part of the universal anomalous dimension, we confirm previous results.
Highlights
We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twisttwo operators in N 1⁄4 4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18
The AdS=CFT correspondence [1,2,3], known as holographic duality, has been one of the most active and tantalizing research topics in high-energy theory over the past two decades. This implies that quantum gravity in anti–de Sitter space, with constant negative curvature, is equivalent to a lower-dimensional nongravitational quantum field theory of conformal type, N 1⁄4 4 supersymmetric Yang-Mills (SYM) theory, living on the boundary of that gravitational space
Investigations of the AdS=CFT correspondence have largely been confined to the planar limit, in which Feynman diagrams of planar topologies contribute, while nonplanar topologies are far more difficult to tackle
Summary
We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twisttwo operators in N 1⁄4 4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. Oðα4sÞ in the strong-coupling constant αs, the quark cusp anomalous dimension in the planar limit has been found via the quark form factor in Ref. Explicit knowledge of γuniðjÞ for general value of j would unfold the nonplanar anatomy of the anomalous dimensions in N 1⁄4 4 SYM theory.
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