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#### On the Integrability of large N Plane-Wave Matrix Theory

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##### Citation

Klose, T., & Plefka, J. (2004). On the Integrability of large N Plane-Wave Matrix
Theory.* Nuclear Physics B,* *679*(1-2), 127-142.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5065-E

##### 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.