Five-Loop Anomalous Dimension of Twist-Two Operators

TL;DR

This work delivers the complete five-loop anomalous dimension for twist-two operators in planar $\mathcal{N}=4$ SYM by combining the asymptotic Bethe ansatz (ABA) with the first Lüscher wrapping correction. Using reciprocity and a reduced basis of reciprocity-respecting harmonic sums, the authors compute the ABA contribution and then meticulously construct the wrapping correction, including finite-size effects via the corrected quantization condition. The combined result passes stringent tests from the BFKL equation (LO and NLO) and double-logarithmic constraints, providing a robust benchmark for spectral equations in planar AdS/CFT. The analysis also reveals structural patterns in the wrapping term, including a transcendental decomposition involving $\zeta$-values, and confirms that wrapping effects only modify subleading terms at large spin, aligning with theoretical expectations. Overall, the paper supplies a critical high-precision data point for validating all-loop spectral frameworks in AdS/CFT and deepens understanding of finite-size effects in integrable gauge theories.

Abstract

In this article we calculate the five-loop anomalous dimension of twist-two operators in the planar N=4 SYM theory. Firstly, using reciprocity, we derive the contribution of the asymptotic Bethe ansatz. Subsequently, we employ the first finite-size correction for the AdS5xS5 sigma model to determine the wrapping correction. The anomalous dimension found in this way passes all known tests provided by the NLO BFKL equation and double-logarithmic constraints. This result thus furnishes an infinite number of experimental data for testing the veracity of the recently proposed spectral equations for planar AdS/CFT correspondence.