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Brane geometry and dimer models

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Abstract

The field content and interactions of almost all known gauge theories in AdS5/CFT4 can be expressed in terms of dimer models or bipartite graphs drawn on a torus. Associated with the fundamental cell is a complex structure parameter τ R . Based on the brane realization of these theories, we can specify a special Lagrangian (SLag) torus fibration that is the natural candidate to be identified as the torus on which the dimer lives. Using the metrics known in the literature, we compute the complex structure τ G of this torus. For the theories on ℂ3 and the conifold and for orbifolds thereof τ R = τ G . However, for more complicated examples, we show that the two complex structures cannot be equal and yet, remarkably, differ only by a few percent. We leave the explanation for this extraordinary proximity as an open challenge.

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Authors and Affiliations

  1. Department of Mathematics, City University, London, Northampton Square, London, EC1V 0HB, U.K.

    Yang-Hui He

  2. School of Physics, NanKai University, Tianjin, 300071, P.R. China

    Yang-Hui He

  3. Merton College, University of Oxford, Oxford, OX1 4JD, U.K.

    Yang-Hui He

  4. NITheP, School of Physics, and Centre for Theoretical Physics, University of the Witwatersrand, Johannesburg, WITS 2050, South Africa

    Vishnu Jejjala

  5. Department of Physics, Technion, Haifa, 3200, Israel

    Diego Rodriguez-Gomez

Authors
  1. Yang-Hui He
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  2. Vishnu Jejjala
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  3. Diego Rodriguez-Gomez
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Correspondence to Vishnu Jejjala.

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ArXiv ePrint: 1204.1065

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He, YH., Jejjala, V. & Rodriguez-Gomez, D. Brane geometry and dimer models. J. High Energ. Phys. 2012, 143 (2012). https://doi.org/10.1007/JHEP06(2012)143

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  • DOI: https://doi.org/10.1007/JHEP06(2012)143

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