On the Integrability of large N Plane-Wave Matrix Theory

TL;DR

This paper demonstrates three-loop integrability of large N plane-wave matrix theory in a specific subsector, confirming its connection to N=4 Super Yang-Mills and supporting the conjecture of three-loop integrability in the planar limit.

Contribution

It provides the first three-loop evidence of integrability in large N plane-wave matrix theory and links it explicitly to the dilatation operator of N=4 SYM in a particular subsector.

Findings

Three-loop degeneracy of parity pairs is preserved.

Effective Hamiltonian matches N=4 SYM dilatation operator after renormalization.

Supports three-loop integrability conjecture in planar N=4 SYM.

Abstract

We show the three-loop integrability of large N plane-wave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory's Hamiltonian in perturbation theory and taking the large N limit. At one-loop level the result is known to be equal to the Heisenberg spin-1/2 chain, which is a well-known integrable system. Here, integrability implies the existence of hidden conserved charges and results in a degeneracy of parity pairs in the spectrum. In order to confirm integrability at higher loops, we show that this degeneracy is not lifted and that (corrected) conserved charges exist. Plane-wave matrix theory is intricately connected to N=4 Super Yang-Mills, as it arises as a consistent reduction of the gauge theory on a three-sphere. We find that after appropriately renormalizing the mass parameter of the plane-wave matrix theory the effective Hamiltonian is identical to the dilatation operator of N=4 Super Yang-Mills theory in the considered subsector. Our results therefore represent a strong support for the conjectured three-loop integrability of planar N=4 SYM and are in disagreement with a recent dual string theory finding. Finally, we study the stability of the large N integrability against nonsupersymmetric deformations of the model.