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A double coset ansatz for integrability in AdS/CFT

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Abstract

We give a proof that the expected counting of strings attached to giant graviton branes in AdS 5 × S 5, as constrained by the Gauss Law, matches the dimension spanned by the expected dual operators in the gauge theory. The counting of string-brane configurations is formulated as a graph counting problem, which can be expressed as the number of points on a double coset involving permutation groups. Fourier transformation on the double coset suggests an ansatz for the diagonalization of the one-loop dilatation operator in this sector of strings attached to giant graviton branes. The ansatz agrees with and extends recent results which have found the dynamics of open string excitations of giants to be given by harmonic oscillators. We prove that it provides the conjectured diagonalization leading to harmonic oscillators.

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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

  2. Centre for Research in String Theory, Department of Physics, Queen Mary University of London, Mile End Road, London, E1 4NS, U.K

    Sanjaye Ramgoolam

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  1. Robert de Mello Koch
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  2. Sanjaye Ramgoolam
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Correspondence to Robert de Mello Koch.

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ArXiv ePrint: 1204.2153

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de Mello Koch, R., Ramgoolam, S. A double coset ansatz for integrability in AdS/CFT. J. High Energ. Phys. 2012, 83 (2012). https://doi.org/10.1007/JHEP06(2012)083

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