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 level superpotential whose matrix model spectral curve develops an Argyres-Douglas singularity. The calculation of the tension of domain walls in the U(nN) theory shows that the standard large N expansion breaks down at the Argyres-Douglas points, with tension that scales as a fractional power of N . Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield the tension of 2-branes in the resulting N = 1 four dimensional non-critical string theories as proposed by Ferrari.