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Nonplanar integrability at two loops

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Abstract

In this article we compute the action of the two loop dilatation operator on restricted Schur polynomials that belong to the su(2) sector, in the displaced corners approximation. In this non-planar large N limit, operators that diagonalize the one loop dilatation operator are not corrected at two loops. The resulting spectrum of anomalous dimensions is related to a set of decoupled harmonic oscillators, indicating integrability in this sector of the theory at two loops. The anomalous dimensions are a non-trivial function of the ’t Hooft coupling, with a spectrum that is continuous and starting at zero at large N, but discreteat finite N.

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Authors and Affiliations

  1. National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics, University of Witwatersrand, Wits, 2050, South Africa

    Robert de Mello Koch, Garreth Kemp, Badr Awad Elseid Mohammed & Stephanie Smith

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  1. Robert de Mello Koch
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  2. Garreth Kemp
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  3. Badr Awad Elseid Mohammed
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  4. Stephanie Smith
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Correspondence to Robert de Mello Koch.

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ArXiv ePrint: 1206.0813

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de Mello Koch, R., Kemp, G., Mohammed, B.A.E. et al. Nonplanar integrability at two loops. J. High Energ. Phys. 2012, 144 (2012). https://doi.org/10.1007/JHEP10(2012)144

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