A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills

TL;DR

The paper develops a novel long-range spin chain to model planar N=4 SYM anomalous dimensions, constructing an all-loop asymptotic Bethe ansatz rooted in a periodized Inozemtsev-like framework and linking it to an inhomogeneous spin-chain form. Through extensive checks up to five loops, the authors demonstrate firm agreement with gauge-theory spectra for multiple excitations and the BMN limit, while exposing subtle three-loop gauge–string mismatches that motivate a limit-order and wrapping-interaction interpretation. They also establish structural parallels between gauge and string descriptions via rapidity/φ-planes and resolvent formalisms, showing the local charge densities align across frameworks even when global Bethe equations differ. The proposed resolution emphasizes summing perturbative gauge theory before taking the thermodynamic limit and incorporating wrapping corrections, aiming to reconcile the gauge/string discrepancy and guide the all-loop formulation. Overall, the work advances integrability-based techniques for computing planar N=4 SYM dimensions and clarifies where string-theory comparisons require refined limiting procedures.

Abstract

We probe the long-range spin chain approach to planar N=4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the SU(2) subsector of the state space up to three loops, but ceases to exhibit the conjectured thermodynamic scaling properties at higher orders. We indicate how this may be bypassed while nevertheless preserving integrability, and suggest the corresponding all-loop asymptotic Bethe ansatz. We also propose the local part of the all-loop gauge transfer matrix, leading to conjectures for the asymptotically exact formulae for all local commuting charges. The ansatz is finally shown to be related to a standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical string theory uncovers a detailed, non-perturbative agreement between the corresponding expressions for the infinite tower of local charge densities. However, the respective Bethe equations differ slightly, and we end by refining and elaborating a previously proposed possible explanation for this disagreement.

Figures (1)

• Figure 1: A possible explanation for both the near BMN and the FT spinning strings disagreement. $F_\ell$ excludes gauge theory wrapping effects, while $G_\ell$ is expected to include them.