An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.
On the nature of the finite-temperature transition in QCD
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abstract
We discuss the nature of the finite-temperature transition in QCD with N_f massless flavors. Universality arguments show that a continuous (second-order) transition must be related to a 3-D universality class characterized by a complex N_f X N_f matrix order parameter and by the symmetry-breaking pattern [SU(N_f)_L X SU(N_f)_R]/Z(N_f)_V -> SU(N_f)_V/Z(N_f)_V, or [U(N_f)_L X U(N_f)_R]/U(1)_V -> U(N_f)_V/U(1)_V if the U(1)_A symmetry is effectively restored at T_c. The existence of any of these universality classes requires the presence of a stable fixed point in the corresponding 3-D Phi^4 theory with the expected symmetry-breaking pattern. Otherwise, the transition is of first order. In order to search for stable fixed points in these Phi^4 theories, we exploit a 3-D perturbative approach in which physical quantities are expanded in powers of appropriate renormalized quartic couplings. We compute the corresponding Callan-Symanzik beta-functions to six loops. We also determine the large-order behavior to further constrain the analysis. No stable fixed point is found, except for N_f=2, corresponding to the symmetry-breaking pattern [SU(2)_L X SU(2)_R]/Z(2)_V -> SU(2)_V/Z(2)_V equivalent to O(4) -> O(3). Our results confirm and put on a firmer ground earlier analyses performed close to four dimensions, based on first-order calculations in the framework of the epsilon=4-d expansion. These results indicate that the finite-temperature phase transition in QCD is of first order for N_f>2. A continuous transition is allowed only for N_f=2. But, since the theory with symmetry-breaking pattern [U(2)_L X U(2)_R]/U(1)_V -> U(2)_V/U(1)_V does not have stable fixed points, the transition can be continuous only if the effective breaking of the U(1)_A symmetry is sufficiently large.
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A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
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Does hot QCD have a conformal manifold in the chiral limit?
An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.