Multicritical points of unoriented random surfaces
Aug 7, 199041 pages
Part of The Large N expansion in quantum field theory and statistical physics: From spin systems to two-dimensional gravity, 513-553
Published in:
- Nucl.Phys.B 350 (1991) 513-553
- Published: 1991
Report number:
- LPS-ENS-245,
- RU-90-39
View in:
Citations per year
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
References(25)
Figures(0)