Hints of integrability beyond the planar limit: nontrivial backgrounds

Koch, Robert de Mello; Dey, Tanay K.; Ives, Norman; Stephanou, Michael

doi:10.1007/jhep01(2010)014

Cited by 12 publications

(9 citation statements)

References 53 publications

(75 reference statements)

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“…This remarkably simple result was confirmed holographically [21] by matching to graviton dynamics in the LLM geometries using the formalism of [22]. For near-BPS operators corresponding to BMN loops [23] it was argued in [24,25,26] that the usual 't Hooft coupling g 2 Y M N is replaced by the effective 't Hooft coupling g 2 Y M (N + M). For additional interesting related studies see [20,27].…”

Section: Introductionmentioning

confidence: 73%

Surprisingly simple spectra

Comarmond

Koch

Jefferies

2011

J. High Energ. Phys.

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103

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The large N limit of the anomalous dimensions of operators in N = 4 super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that have two columns (both long) so that the classical dimension of these operators is O(N). At large N these two column operators mix with each other but are decoupled from operators with n = 2 columns. The planar approximation does not capture the large N dynamics. For operators built with 2, 3 or 4 impurities the dilatation operator is explicitly evaluated. In all three cases, in a certain limit, the dilatation operator is a lattice version of a second derivative, with the lattice emerging from the Young diagram itself. The one loop dilatation operator is diagonalized numerically. All eigenvalues are an integer multiple of 8g 2 Y M and there are interesting degeneracies in the spectrum. The spectrum we obtain for the one loop anomalous dimension operator is reproduced by a collection of harmonic oscillators. This equivalence to harmonic oscillators generalizes giant graviton results known for the BPS sector and further implies that the Hamiltonian defined by the one loop large N dilatation operator is integrable. This is an example of an integrable dilatation operator, obtained by summing both planar and non-planar diagrams.

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Section: Introductionmentioning

confidence: 73%

Surprisingly simple spectra

Comarmond

Koch

Jefferies

2011

J. High Energ. Phys.

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103

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“…We will give an example of a closed string excitation. For relevant earlier literature see [49,50,51,52].…”

Section: Strong Coupling Cftmentioning

confidence: 99%

Exciting LLM geometries

Koch

Huang

Tribelhorn

2018

J. High Energ. Phys.

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We study excitations of LLM geometries. These geometries arise from the backreaction of a condensate of giant gravitons. Excitations of the condensed branes are open strings, which give rise to an emergent Yang-Mills theory at low energy. We study the dynamics of the planar limit of these emergent gauge theories, accumulating evidence that they are planar N = 4 super Yang-Mills. There are three observations supporting this conclusion: (i) we argue for an isomorphism between the planar Hilbert space of the original N = 4 super Yang-Mills and the planar Hilbert space of the emergent gauge theory, (ii) we argue that the OPE coefficients of the planar limit of the emergent gauge theory vanish and (iii) we argue that the planar spectrum of anomalous dimensions of the emergent gauge theory is that of planar N = 4 super Yang-Mills. Despite the fact that the planar limit of the emergent gauge theory is planar N = 4 super Yang-Mills, we explain why the emergent gauge theory is not N = 4 super Yang-Mills theory. 1 robert@neo.phys.wits.ac.za

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“…On the dual gravity side the number of D3-branes is so large that it is no longer possible to ignore backreaction, and this modifies the AdS geometry into an LLM-type background. Strings "attached" to the above operators 20 have recently been considered from the gauge theory side in [109]. It is possible to integrate out the effect of the background and construct an effective dilatation operator, which is integrable in a certain limit.…”

Section: Operators With Very Large R-chargementioning

confidence: 99%