Quark Matter with a Chiral Chemical Potential

In this talk, we report the results discussed in [1], related to the phase structure of hot quark matter in presence of a background of chiral charge density, n5. The latter is introduced in the simplest way possible, namely by virtue of a chemical potential, μ5, conjugated to n5. In more detail, after a brief introduction and list of motivations of this kind of study, we discuss the interplay between chiral symmetry restoration and deconfinement at finite μ5, as well as the critical endpoint in the phase diagram and its possible relationship with the critical endpoint of the phase diagram od Quantum Chromodynamics (QCD). In the talk, due to time limitation, we can emphasize few results related to the latter topic. Therefore we need to leave apart several applications of the ideas, as well as of the formalism, developed here to the physics of heavy ion collisions, with particular reference to the Chiral Magnetic Effect [2, 3, 4]. The latter might be relevant for the phenomenology of heavy ion collisions, because a copious production of gluon configurations, the QCD sphalerons, with a finite winding number is expected in the quark-gluon-plasma phase of QCD, see [5] and references therein. Because of the chiral Ward identity, the interaction of the sphalerons with the quarks causes a chirality change of the latters. As a consequence, a copious production of local domains in which chirality is imbalanced, is expected in the quark-gluon-plasma. The critical endpoint, CP, of QCD [6] is the cornerstone of the phase diagram of strongly interacting matter. At CP, a crossover line and a first order line are supposed to intercept. It is thus not surprising that an intense experimental activity is nowadays dedicated to the detection of such a point, which involves the large facilities at RHIC and LHC; moreover, further experiments are expected after the development of FAIR at GSI. Several theoretical signatures of CP have been suggested [7, 8]. Despite the importance of CP, a firm theoretical evidence of its existence is still missing. In fact, the sign problem makes the Lattice Monte Carlo simulations difficult, if not impossible, in the large baryon-chemical potential (μ) region for Nc = 3 [9], see [10] for a recent review. Therefore, it has not yet been possible to prove unambiguously the existence and the location of CP starting from first principles simulations of grand-canonical ensembles. Moreover, the predictions of effective models are spread in the T − μ plane, see for example [11, 12].