Multicut criticality in the Penner model and c=1 strings. (English) Zbl 0813.57028
Catto, Sultan (ed.) et al., Differential geometric methods in theoretical physics. Proceedings of the 20th international conference, June 3-7, 1991, New York City, NY, USA. Vol. 1-2. Singapore: World Scientific. 715-726 (1992).
Summary: The steepest descent solution of the \(m\)-th critical point of the Penner matrix model has an \(m\)-component eigenvalue support, consisting of symmetrically placed arcs in the complex eigenvalue plane. Criticality results when the branch points of this support coalesce in pairs to form a closed contour. We derive the string equations of these matrix models for arbitrary \(m\), using the orthogonal polynomial method. The double- scaled continuum solutions are described by nonlinear finite-difference equations. The free energy of the \(m\)-th model is shown to be the Legendre transform of the free energy of the \(c = 1\) string compactified to a circle of radius equal to an integer multiple, \(m\), of the self dual radius.
For the entire collection see [Zbl 0801.00032].
For the entire collection see [Zbl 0801.00032].
MSC:
| 57R57 | Applications of global analysis to structures on manifolds |
| 57R70 | Critical points and critical submanifolds in differential topology |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
