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Hot Quark Matter with an Axial Chemical Potential

We analyze the phase diagram of hot quark matter in presence of an axial chemical potential, $μ_5$. The latter is introduced to mimic the chirality transitions induced, in hot Quantum Chromodynamics, by the strong sphaleron configurations. In particular, we study the curvature of the critical line at small $μ_5$, the effects of a finite quark mass and of a vector interaction. Moreover, we build the mixed phase at the first order phase transition line, and draw the phase diagram in the chiral density and temperature plane. We finally compute the full topological susceptibility in presence of a background of topological charge.