Theoretical and Mathematical Physics

, Volume 169, Issue 1, pp 1405–1412 | Cite as

Low-dimensional Yang-Mills theories: Matrix models and emergent geometry

Article
First Online:

Abstract

In a simple example of a bosonic three-matrix model, we show how a background geometry can condense as the temperature or coupling constant passes through a critical value. We show that this example belongs to a new universality class of phase transitions where the background geometry is itself emergent.

Keywords

matrix model emergent geometry dimer model 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Phys. Rep., 323, 183–386 (2000); arXiv:hepth/9905111v3 (1999).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, Phys. Rev. D, 55, 5112–5128 (1997); arXiv:hep-th/9610043v3 (1996).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    N. Ishibashi, H. Kawai, Y. Kitazawa, and A. Tsuchiya, Nucl. Phys. B, 498, 467–491 (1997); arXiv:hep-th/9612115v2 (1996).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    H. Steinacker, Class. Q. Grav., 27, 133001 (2010); arXiv:1003.4134v5 [hep-th] (2010).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    F. A. Berezin, Comm. Math. Phys., 40, 153–174 (1975).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    J. Hoppe, “Quantum theory of a massless relativistic surface and a two-dimensional bound state problem,” Doctoral dissertation, Massachusetts Inst. of Technology, Cambridge, Mass. (1982).Google Scholar
  7. 7.
    J. Madore, Class. Q. Grav., 9, 69–87 (1992).MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    A. Connes, Noncommutative Geometry, Acad. Press, San Diego, Calif. (1994).MATHGoogle Scholar
  9. 9.
    R. Delgadillo-Blando, D. O’Connor, and B. Ydri, Phys. Rev. Lett., 100, 201601 (2008); arXiv:0712.3011v2 [hep-th] (2007).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    R. Delgadillo-Blando, D. O’Connor, and B. Ydri, JHEP, 0905, 049 (2009); arXiv:0806.0558v4 [hep-th] (2008).MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    A. Pelissetto and E. Vicari, Phys. Rep., 368, 549–727 (2002); arXiv:cond-mat/0012164v6 (2000).MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    J. F. Nagle, C. S. O. Yokoi, and S. M. Bhattacharjee, “Dimer models on anisotropic lattices,” in: Phase Transitions and Critical Phenomena (C. Domb and J. L. Lebowitz, eds.), Vol. 13, Acad. Press, London (1989), pp. 235–297.Google Scholar
  13. 13.
    C. Nash and D. O’Connor, J. Phys A, 42, 012002 (2009); arXiv:0809.2960v3 [hep-th] (2008).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.School of Theoretical PhysicsDublin Institute for Advanced StudiesDublinIreland

Personalised recommendations