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

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