Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory

Abstract

We compute the general form of the six-loop anomalous dimension of twist-two operators with arbitrary spin in planar N=4 SYM theory. First we find the contribution from the asymptotic Bethe ansatz. Then we reconstruct the wrapping terms from the first 35 even spin values of the full six-loop anomalous dimension computed using the quantum spectral curve approach. The obtained anomalous dimension satisfies all known constraints coming from the BFKL equation, the generalised double-logarithmic equation, and the small spin expansion.

arXiv comment33 pages, 4 ancillary files, minor changes

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• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• BFKL pomeron in the next-to-next-to-leading approximation in the planar N=4 SYM theory
• Worldsheet dilatation operator for the $AdS$ superstring
• Exact result in N=4 SYM theory: Generalised double-logarithmic equation
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• NNNLLA BFKL pomeron eigenvalue in the planar N=4 SYM theory
• Spin-$s$ $Q$-systems: Twist and Open Boundaries