Communications in Mathematical Physics

, Volume 179, Issue 1, pp 235–256 | Cite as

Almost flat planar diagrams

  • Vladimir A. Kazakov
  • Matthias Staudacher
  • Thomas Wynter
Article

Abstract

We continue our study of matrix models of dually weighted graphs. Among the attractive features of these models is the possibility to interpolate between ensembles of regular and random two-dimensional lattices, relevant for the study of the crossover from two-dimensional flat space to two-dimensional quantum gravity. We further develop the formalism of largeN character expansions. In particular, a general method for determining the largeN limit of a character is derived. This method, aside from being potentially useful for a far greater class of problems, allows us to exactly solve the matrix models of dually weighted graphs, reducing them to a well-posed Riemann-Hilbert problem. The power of the method is illustrated by explicitly solving a new model in which only positive curvature defects are permitted on the surface, an arbitrary amount of negative curvature being introduced at a single insertion.

Keywords

Attractive Feature Quantum Gravity Matrix Model Quantum Computing Weighted Graph 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brézin, E., Itzykson, C., Parisi, G., Zuber, J.-B.: Commun. Math. Phys.59, 35 (1978)CrossRefGoogle Scholar
  2. 2.
    Di Francesco, P., Itzykson, C.: Ann. Inst. Henri. Poincaré59, no. 2, 117 (1993)Google Scholar
  3. 3.
    Itzykson, C., Züber, J.-B.: J. Math. Phys.,21(3), 411 (1980)CrossRefGoogle Scholar
  4. 4.
    Kazakov, V.A., Staudacher, M., Wynter, T.: École Normale preprint LPTENS-95/9, Commun. Math. Phys., to appearGoogle Scholar
  5. 5.
    David, F.: Nucl. Phys.B257, 45 (1985)CrossRefGoogle Scholar
  6. 6.
    Kazakov, V.A.: Phys. Lett.B150, 282 (1985)CrossRefGoogle Scholar
  7. 7.
    Fröhlich, J.: In: Lecture Notes in Physics, Vol.216, Berlin, Heidelberg, New York: Springer, 1985; Ambjørn, J., Durhuus, B., Fröhlich, J.: Nucl. Phys.B257 [FS14], 433 (1985)Google Scholar
  8. 8.
    Byrd, P.F., Friedman, M.D.: Handbook of Elliptic Integrals for Engineers and Physicists. Berlin, Heidelberg, New York: Springer, 1954Google Scholar
  9. 9.
    Lawden, D.F.: Elliptic Functions and Applications. Berlin, Heidelberg, New York: Springer, 1989Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Vladimir A. Kazakov
    • 1
  • Matthias Staudacher
    • 1
  • Thomas Wynter
    • 1
  1. 1.Laboratoire de Physique Théorique de l'École Normale SupérieureParis Cedex 05France

Personalised recommendations