Publication : t92/159

Non-perturbative effects in matrix models and vacua of two dimensional gravity

David F. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
The most general large $N$ eigenvalues distribution for the one matrix model is shown to consist of tree-like structures in the complex plane. For the $m=2$ critical point, such a solution describes the strong coupling phase of $2d$ quantum gravity ($c=0$ non-critical string). It is obtained by taking combinations of complex contours in the matrix integral, and the relative weight of the contours is identified with the non-perturbative ``$\theta$-parameter" that fixes uniquely the solution of the string equation (Painlev\'e I). This allows to recover by instanton methods results on the non-perturbative effects obtained by the Isomonodromic Deformation Method, and to construct for each $\theta$-vacuum the observables (the loop correlation functions) which satisfy the loop equations. The breakdown of analyticity of the large $N$ solution is related to the existence of poles for the loop operators.
Année de publication : 1993
Revue : Phys. Lett. B 302 403-410 (1993)
Preprint : arXiv:hep-th/9212106
Langue : Anglais

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