Matrix Models, Argyres-Douglas singularities and double scaling limits

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Abstract
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 scaling 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.

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