Low mu and imaginary mu signals of a critical point in the phase diagram of an exactly soluble chiral symmetry breaking theory

Holography has allowed the exact solution of a small number of large Nc gauge theories. Amongst these is an N=2 SYM theory of quarks interacting with N=4 gauge fields. The temperature chemical potential phase diagram for this theory in the presence of a magnetic field is exactly known and shows first and second order chiral symmetry restoration transitions and a critical point. Here we extend this phase diagram to imaginary chemical potential to seek structure at small real mu and imaginary mu that help to reconstruct the large real mu phase structure. We also explore a phenomenologically deformed version of the theory where the critical point can be moved into the imaginary chemical potential plane. In particular we observe that when the transition is second order in these theories there are naturally two distinct transitions - one for the onset of density and one for chiral symmetry restoration. In addition, the phase diagram has boundaries of regions where metastable vacua exist and these boundaries, as well as the phase boundaries, converge at the critical point. These observations may point to techniques for the study of the QCD critical point either on the lattice or using heavy ion collision data.