Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM

TL;DR

This work applies the quantum spectral curve, via the ${\bf P}\mu$-system, to twist operators in planar ${\cal N}=4$ SYM and develops a controlled small-spin expansion. The authors derive the exact slope function $\\gamma^{(1)}(g)$ for arbitrary coupling and extend the analysis to the curvature function $\\gamma^{(2)}(g)$, providing closed-form double-contour integral expressions for $J=2,3,4$ that capture wrapping and dressing effects. They implement an iterative small-$S$ procedure to obtain the curvature, enabling precise weak- and strong-coupling checks, including a new strong-coupling coefficient for the Konishi dimension and additional BFKL intercept terms. A prescription for analytic continuation in $S$ links AdS/CFT integrability with the BFKL regime, suggesting a path to deriving BFKL behavior from the ${\bf P}\mu$-system and systematizing finite-size effects across the spectrum.

Abstract

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.