Analysis of supersymmetric field theories via AdS/CFT, brane setups and matrix models

Abstract

N = 1 theories whose matrix model spectral curve develops Argyres-Douglas singularities are constructed. The large N expansion breaks down at the critical points with domain wall tensions scaling as a fractional power of N. However, there exist double scaling limits that are conjectured to define a four-dimensional non-critical string theory. The confinement-deconfinement phase transition in 3d = 1 U(N) Super Yang-Mills Chern-Simons theory is studied via its supergravity dual description. The would-be deconfined higher temperature phase is actually unstable. Therefore, it is not possible to conclude whether the transition takes place or not. The splitting of NS5-branes and D(p+2)-branes on orientifold Op-planes is analyzed. The rules governing this process are derived and checked in the case p = 4 by means of Seiberg-Witten curves.