On the breakdown of perturbative integrability in large N matrix models

Abstract

We study the perturbative integrability of the planar sector of a massive SU(N) matrix quantum mechanical theory with global SO(6) invariance and Yang-Mills-like interaction. This model arises as a consistent truncation of maximally supersymmetric Yang-Mills theory on a three-sphere to the lowest modes of the scalar fields. In fact, our studies mimic the current investigations concerning the integrability properties of this gauge theory. Like in the field theory we can prove the planar integrability of the SO(6) model at first perturbative order. At higher orders we restrict ourselves to the widely studied SU(2) subsector spanned by two complexified scalar fields of the theory. We show that our toy model satisfies all commonly studied integrability requirements such as degeneracies in the spectrum, existence of conserved charges and factorized scattering up to third perturbative order. These are the same qualitative features as the ones found in super Yang-Mills theory, which were enough to conjecture the all-loop integrability of that theory. For the SO(6) model, however, we show that these properties are not sufficient to predict higher loop integrability. In fact, we explicitly demonstrate the breakdown of perturbative integrability at fourth order.

27 pages

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Cited by in corpus (6)

• Classical Open String Integrability
• Chaos in the BMN matrix model
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Aspects of Integrability in AdS/CFT Duality