Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory -: art. no. 085013

We study the physics of N=1 super Yang-Mills theory with the gauge group U(N) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large N expansion is singular near the critical points, with domain wall tensions scaling as a fractional power of N. We argue that the critical points are four-dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four-dimensional noncritical string theory. D-brane states can be deformed continuously into closed string solitonic states, and vice versa, along paths that go over regions where the string coupling is strong.