Phases of Thermal N=2 Quiver Gauge Theories

We consider large N U(N)^M thermal N=2 quiver gauge theories on S^1 x S^3. We obtain a phase diagram of the theory with R-symmetry chemical potentials, separating a low-temperature/high-chemical potential region from a high-temperature/low-chemical potential region. In close analogy with the N=4 SYM case, the free energy is of order O(1) in the low-temperature region and of order O(N^2 M) in the high-temperature phase. We conclude that the N=2 theory undergoes a first order Hagedorn phase transition at the curve in the phase diagram separating these two regions. We observe that in the region of zero temperature and critical chemical potential the Hilbert space of gauge invariant operators truncates to smaller subsectors. We compute a l-loop effective potential with non-zero VEV's for the scalar fields in a sector where the VEV's are homogeneous and mutually commuting. At low temperatures the eigenvalues of these VEV's are distributed uniformly over an S^5/Z_M which we interpret as the emergence of the S^5/Z_M factor of the holographically dual geometry AdS_5 x S^5/Z_M. Above the Hagedorn transition the eigenvalue distribution of the Polyakov loop opens a gap, resulting in the collapse of the joint eigenvalue distribution from S^5/Z_M x S^1 into S^6/Z_M.