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Dynamical tachyons on fuzzy spheres

David Berenstein1,2,* and Diego Trancanelli1,3,†

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 2Institute for Advanced Study, School of Natural Science, Princeton, New Jersey 08540, USA
  • 3Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA

  • *dberens@physics.ucsb.edu
  • †dtrancan@physics.wisc.edu
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Phys. Rev. D 83, 106001 – Published 3 May, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.106001

Abstract

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the Berenstein-Maldacena-Nastase plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles, classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills theory on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.

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Phys. Rev. D 83, 106001– Published 3 May, 2011
  • Received 22 February 2011

© 2011 American Physical Society

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