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From Large N Nonplanar Anomalous Dimensions to Open Spring Theory · Around

2011

From Large N Nonplanar Anomalous Dimensions to Open Spring Theory

Koch, Robert de Mello, Kemp, Garreth, Smith, Stephanie

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In this note we compute the non-planar one loop anomalous dimension of restricted Schur polynomials that have a bare dimension of O(N).

This is achieved by mapping the restricted Schur polynomials into states of a specific U(N) irreducible representation.
In this way the dilatation operator is mapped into a u(n) valued operator and, as a result, can easily be diagonalized.
The resulting spectrum is reproduced by a classical model of springs between masses.

Built on

T. W. Brown, P. J. Heslop, S. Ramgoolam, “Diagonal free field matrix correlators, global symmetries and giant gravitons,” JHEP 0904
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S. Corley, A. Jevicki, S. Ramgoolam, “Exact correlators of giant gravitons from dual N=4 SYM theory,” Adv. Theor. Math. Phys. 5
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S. Corley, S. Ramgoolam, “Finite factorization equations and sum rules for BPS correlators in N=4 SYM theory,” Nucl. Phys. B641
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N. Beisert, C. Kristjansen and M. Staudacher, “The dilatation operator of N = 4 super Yang-Mills theory,” Nucl. Phys. B 664
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Then

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R. Bhattacharyya, R. de Mello Koch, M. Stephanou, “Exact Multi-Restricted Schur Polynomial Correlators,” JHEP 0806

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