Matrix models, Argyres-Douglas singularities and double scaling limits

We construct an N=1 theory with gauge group U(nN) and degree n+1 tree levelsuperpotential whose matrix model spectral curve develops an A_{n+1}Argyres-Douglas singularity. We evaluate the coupling constants of thelow-energy U(1)^n theory and show that the large N expansion is singular at theArgyres-Douglas points. Nevertheless, it is possible to define appropriatedouble scaling limits which are conjectured to yield four dimensionalnon-critical string theories as proposed by Ferrari. In the Argyres-Douglaslimit the n-cut spectral curve degenerates into a solution with n/2 cuts foreven n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been corrected and the calculation of the coupling constants of the low-energy theory has been adde