Graph duality as an instrument of Gauge-String correspondence

Pablo Diaz University of Lethbridge Hai Lin Tsinghua University Alvaro Veliz-Osorio University of the Witwatersrand

Mathematical Physics mathscidoc:1702.22017

J.Math.Phys., 57, (5), 052302, 2016.5
We explore an identity between two branching graphs and propose a physical meaning in the context of the gauge-gravity correspondence. From the mathematical point of view, the identity equates probabilities associated with GT, the branching graph of the unitary groups, with probabilities associated with Y, the branching graph of the symmetric groups. In order to furnish the identity with physical meaning, we exactly reproduce these probabilities as the square of three point functions involving certain hook-shaped backgrounds. We study these backgrounds in the context of LLM geometries and discover that they are domain walls interpolating two AdS spaces with different radii. We also find that, in certain cases, the probabilities match the eigenvalues of some observables, the embedding chain charges. We finally discuss a holographic interpretation of the mathematical identity through our results.
Gauge-String correspondence, branching graphs, Young Graph, Gelfand-Tsetlin Graph, correlation functions
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  title={Graph duality as an instrument of Gauge-String correspondence},
  author={Pablo Diaz, Hai Lin, and Alvaro Veliz-Osorio},
Pablo Diaz, Hai Lin, and Alvaro Veliz-Osorio. Graph duality as an instrument of Gauge-String correspondence. 2016. Vol. 57. In J.Math.Phys.. pp.052302.
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