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

Abstract

Holography has allowed the exact solution of a small number of largeNcgauge theories. Amongstthese is anN=2 SYM theory of quarks interacting withN=4 gauge fields. The temperature chemicalpotential phase diagram for this theory in the presence of a magnetic field is exactly known andshows first and second order chiral symmetry restoration transitions and a critical point. Herewe extend this phase diagram to imaginary chemical potential to seek structure at small realμand imaginaryμthat help to reconstruct the large realμphase structure. We also explore aphenomenologically deformed version of the theory where the critical point can be moved into theimaginary chemical potential plane. In particular we observe that when the transition is secondorder in these theories there are naturally two distinct transitions - one for the onset of densityand one for chiral symmetry restoration. In addition, the phase diagram has boundaries of regionswhere metastable vacua exist and these boundaries, as well as the phase boundaries, converge atthe 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.

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