Integrability and Transcendentality
B.Eden, M.Staudacher

TL;DR
This paper derives a two-loop Bethe ansatz for N=4 gauge theory, analyzes an all-loop asymptotic ansatz, and predicts a universal scaling function for large-spin operators, linking gauge theory and string theory results.
Contribution
It introduces a novel all-loop scaling function obeying transcendentality principles, connecting perturbative gauge theory with string theory predictions.
Findings
Derivation of the two-loop Bethe ansatz for sl(2) sector.
Proposal of a universal all-loop scaling function.
Qualitative agreement with string theory at strong coupling.
Abstract
We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of N=4 gauge theory directly from the field theory. We then analyze a recently proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large spacetime spin at large but finite twist, and find a novel all-loop scaling function. This function obeys the Kotikov-Lipatov transcendentality principle and does not depend on the twist. Under the assumption that one may extrapolate back to leading twist, our result yields an all-loop prediction for the large-spin anomalous dimensions of twist-two operators. The latter also appears as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov for the all-loop structure of the maximally helicity violating (MHV) n-point gluon amplitudes of N=4 gauge theory. This potentially establishes a direct link between the worldsheet and the spacetime S-matrix…
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