Planar N=4 Gauge Theory and the Hubbard Model

TL;DR

This paper connects the integrable long-range spin chain describing N=4 gauge theory to the Hubbard model, revealing a new perspective on the gauge theory's structure and its relation to condensed matter models.

Contribution

It identifies the long-range spin chain as an approximation to the Hubbard model, bridging gauge theory integrability with condensed matter physics.

Findings

The spin chain matches the Hubbard model in certain limits.

The model exhibits BMN scaling to all orders in perturbation theory.

Provides a new framework for understanding N=4 gauge theory through condensed matter models.

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.