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Fuzzy scalar field theory as matrix quantum mechanics

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Abstract

We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed external matrices. These terms can be approximated by multitrace expressions using a group theoretical method developed recently. The resulting matrix model is accessible to the standard techniques of matrix quantum mechanics.

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Authors and Affiliations

  1. Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, RJ, Brasil

    Matthias Ihl

  2. Fachbereich Mathematik, Bereich Algebra und Zahlentheorie, Universität Hamburg, D-20146, Hamburg, Deutschland

    Christoph Sachse

  3. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, U.K.

    Christian Sämann

  4. Maxwell Institute for Mathematical Sciences, Edinburgh, U.K.

    Christian Sämann

Authors
  1. Matthias Ihl
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  2. Christoph Sachse
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  3. Christian Sämann
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Correspondence to Christian Sämann.

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ArXiv ePrint:1012.3568

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Ihl, M., Sachse, C. & Sämann, C. Fuzzy scalar field theory as matrix quantum mechanics. J. High Energ. Phys. 2011, 91 (2011). https://doi.org/10.1007/JHEP03(2011)091

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