Does the chiral magnetic effect change the dynamic universality class in QCD?

Abstract

In QCD matter under an external magnetic field, the chiral magnetic effect (CME) leads to the collective gapless mode called the chiral magnetic wave (CMW). Since dynamic universality class generally depends on low-energy gapless modes, it is nontrivial whether the CME and the resulting CMW change that of the second-order chiral phase transition in QCD. To address this question, we study the critical dynamics near the chiral phase transition in massless two-flavor QCD under an external magnetic field. By performing the dynamic renormalization-group analysis within the expansion, we find that the presence of the CME changes the dynamic universality class to that of model A. We also show that the transport coefficient of the CME is not renormalized by the critical fluctuations of the order parameter. arXiv:1803.07267v2 [hep-ph] 23 Nov 2018 11 The susceptibility χ is denoted as C in ref. [44].

Critical Dynamics of Massless QCD with the Chiral Magnetic Effect

“…In this proceedings, we report on our recent study of the dynamic universality class of the secondorder chiral phase transition in massless two-flavor QCD in the magnetic field [16]. We demonstrate that the presence of the magnetic field with or without the CME modifies the dynamic universality class as shown in Table I.…”

“…(4.36) of Ref. [16]. Recalling that the CMW is the propagating wave of n and n 5 , this vanishing self-energy means that not only n but also n 5 is decoupled from the critical dynamics.…”

“…To describe the low-energy dynamics near the second-order chiral phase transition, we also take into account the conserved charge densities associated with G, i.e., the isospin density n =qγ 0 τ 3 q and the axial isospin density n 5 =qγ 0 γ 5 τ 3 q as low-energy degrees of freedom. Then, the generalized Lagevin equations for ϕ α , n, and n 5 with macroscopic dissipation are given by [16]…”

“…We here omit the explicit forms of F and the FDR, since they are not important in the following arguments (see Ref. [16] for the details). The essential ingredient in our analysis is the following Poisson brackets (PBs) resulting from the classical limit of the corresponding quantum commutators:…”

Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds

“…Instead of the Langevin type description ("event-by-event" description) of fluctuations, also the extension of the hydrodynamics (Hydro+) with slow modes and two-point functions is proposed for the critical dynamics [41]. Another important topic of the hydrodynamic fluctuations is the renormalization of hydrodynamics due to the nonlinear effects of the hydrodynamic fluctuations which are analyzed by various methods in various contexts [42][43][44][45][46][47][48][49][50]. The transport coefficients and the equation of state should be renormalized depending on the cutoff scales of the hydrodynamic fluctuations, and also there arises the long-time tail of the two-point correlations, which cannot be renormalized into ordinary transport coefficients.…”