Multicritical points of unoriented random surfaces

Aug 7, 1990
41 pages
Published in:
  • Nucl.Phys.B 350 (1991) 513-553
  • Published: 1991
Report number:
  • LPS-ENS-245,
  • RU-90-39

Citations per year

1990199920082017202402468
Abstract: (Elsevier)
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/d x 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 ((ϖ 2 + ƒ) m − 1 2 ) + 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.
  • random surface
  • critical phenomena
  • continuum limit
  • matrix model
  • correlation function
  • string model
  • gravitation
  • perturbation theory