Matrix Models, Argyres-Douglas singularities and double scaling limits

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 A_{n+1} Argyres-Douglas singularity. We evaluate the coupling constants of the low-energy U(1)^n theory and show that the large N expansion is singular at the Argyres-Douglas points. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield four dimensional non-critical string theories as proposed by Ferrari. In the Argyres-Douglas limit the n-cut spectral curve degenerates into a solution with n/2 cuts for even n and (n+1)/2 cuts for odd n.

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 added

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Cited by in corpus (8)

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• Non-Critical Superstrings from Four-Dimensional Gauge Theory
• Large N gauge theories and topological cigars
• Double Scaling Limits in Gauge Theories and Matrix Models
• Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models
• Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory
• Double Scaling Limits and Twisted Non-Critical Superstrings