From polymers to quantum gravity: Triple scaling in rectangular random matrix models
Dec 30, 199128 pages
Published in:
- Nucl.Phys.B 390 (1993) 716-746
e-Print:
- hep-th/9112037 [hep-th]
Report number:
- MCGILL-92-01,
- NSF-ITP-91-01,
- IASSNS-HEP-91-93
View in:
Citations per year
Abstract:
Rectangular matrix models can be solved in several qualitatively distinct large limits, since two independent parameters govern the size of the matrix. Regarded as models of random surfaces, these matrix models interpolate between branched polymer behaviour and two-dimensional quantum gravity. We solve such models in a `triple-scaling' regime in this paper, with and becoming large independently. A correspondence between phase transitions and singularities of mappings from to is indicated. At different critical points, the scaling behavior is determined by: i) two decoupled ordinary differential equations; ii) an ordinary differential equation and a finite difference equation; or iii) two coupled partial differential equations. The Painlev\'e II equation arises (in conjunction with a difference equation) at a point associated with branched polymers. For critical points described by partial differential equations, there are dual weak-coupling/strong-coupling expansions. It is conjectured that the new physics is related to microscopic topology fluctuations.- quantum gravity
- dimension: 2
- matrix model
- partition function
- scaling
- field theory: planar
- energy
- critical phenomena
- Korteweg-de Vries equation
- expansion 1/N
References(25)
Figures(0)