Flow of Hagedorn singularities and phase transitions in large N gauge theories

We investigate the singularity structure of the (-1)(F) graded partition function in QCD with n(f) >= 1 massive adjoint fermions in the large-N limit. Here, F is fermion number and N is the number of colors. The large N partition function is made reliably calculable by taking space to be a small three-sphere S-3. Singularities in the graded partition function are related to phase transitions and to Hagedorn behavior in the (-1)(F)-graded density of states. We study the flow of the singularities in the complex inverse temperature beta plane as a function of the quark mass. This analysis is a generalization of the Lee-Yang-Fisher-type analysis for a theory which is always in the thermodynamic limit thanks to the large N limit. We identify two distinct mechanisms for the appearance of physical Hagedorn singularities and center-symmetry changing phase transitions at real positive beta, inflow of singularities from the beta = 0 point, and collisions of complex conjugate pairs of singularities.