On the Integrability of large N Plane-Wave Matrix Theory

Thomas Klose; Jan Plefka

doi:10.1016/j.nuclphysb.2003.11.043

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arXiv · hep-th/0310232

On the Integrability of large N Plane-Wave Matrix Theory

Thomas Klose·Jan Plefka

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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.

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Thomas Klose, Jan Plefka. 2003-11-13. On the Integrability of large N Plane-Wave Matrix Theory. https://doi.org/10.1016/j.nuclphysb.2003.11.043

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