Multicritical points of unoriented random surfaces
Authors:
E. Brezin
Affiliation:
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231, Paris cedex 05, France
Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855, USA
Abstract:
Unoriented surfaces generated by real symmetric one-matrix models are solved in the scaling limit in which the size of the matrix (related to the string coupling constant) goes to infinity and the cosmological constant approaches a multicritical point of a suitably chosen potential. The solution involves skew orthogonal polynomials, and in spite of the non-local character of the operations d/dx or multiplication by x acting on these polynomials, a local differential formalism is shown to be present in this problem as well. The Gel'fand-Dikii pseudo-differential operator appears here factorized as a product of two differential operators of degrees m and (m − 1) respectively. The relations with other ensembles of random matrices are examined and the difficulties associated with multi-matrix models are pointed out.