Publication : t90/090

Phases of the large N matrix model and non-perturbative effects in 2d gravity

David F. ()
The large-N solution of the one-matrix model of E. Brézin, C. Itzykson, G. Parisi and J.-B. Zuber is reconsidered for generic complex potential. A regular large-N limit does not exist in some singular domain, which depends on the prescription chosen in order to make the matrixintegral convergent at infinity. Near the m = 2 critical point the singular domain (in the scaling variable x complex plane) is a sector of angle 2π/5 coinciding with the sector of poles of the “triply truncated” Painlevé I transcendent of Boutroux, which is therefore (although not real) the only solution of the string equation compatible with the matrix model and the loop equations for two-dimensional gravity. Our approach allows us to relate non-perturbative effects in the string equations to instantons in the matrix model and to discuss the flows between multicritical points.
Année de publication : 1991
Revue : Nucl. Phys. B 348 507-524 (1991)
DOI : 10.1016/0550-3213(91)90202-9
Langue : Anglais

Fichier(s) à télécharger :
  • t90-090.pdf
  • phase3.pdf


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