THE PENNER MATRIX MODEL AND C = 1 STRINGS

The steepest descent solution of the Penner matrix model has a one-cut eigenvalue support. Criticality results when the two branch points of this support coalesce. The support is then a closed contour in the complex eigenvalue plane. Simple generalizations of the Penner model have multi-cut solutions. For these models, the eigenvalue support at criticality is also a closed contour, but consisting of several cuts. We solve the simplest such model, which we call the KT model, in the double-scaling limit. Its free energy is a Legendre transform of the free energy of the c = 1 string compactified to the critical radius of the Kosterlitz-Thouless phase transition.