Planar N=4 Gauge Theory and the Hubbard Model

TL;DR

This work shows that the planar N=4 SYM su(2) dilatation operator can be realized as the strong-coupling limit of a twisted Hubbard model, providing a microscopic, finite-L framework that yields the three-loop dilatation operator exactly and reproduces the asymptotic BDS Bethe equations via Lieb–Wu analysis. By treating magnons as bound states of holes and doublons, the authors derive the BDS dispersion and scattering in the large-L limit, while carefully characterizing finite-L wrapping and demi-wrapping corrections. The four-loop Konishi result exposes wrapping at O(g^6), revealing discrepancies with BDS that cannot be eliminated by wrapping corrections within this model. Collectively, the paper demonstrates that BDS is an asymptotic description tied to a specific short-range Hubbard formulation, and suggests that a complete all-loop dilatation operator may require extensions beyond su(2) toward the full psu(2,2|4) structure.

Abstract

Recently it was established that a certain integrable long-range spin chain describes the dilatation operator of N=4 gauge theory in the su(2) sector to at least three-loop order, while exhibiting BMN scaling to all orders in perturbation theory. Here we identify this spin chain as an approximation to an integrable short-ranged model of strongly correlated electrons: The Hubbard model.