Dynamic critical behavior of the chiral phase transition from the real-time functional renormalization group

A bstract The collective dynamics around the second-order O (4) chiral phase transition in QCD with two massless quark flavors can be understood by appealing to universality. We present a novel formulation of the real-time functional renormalization group (FRG) that describes the stochastic hydrodynamic equations of motion for systems in the same dynamic universality class, which corresponds to Model G in the Halperin-Hohenberg classification. Our approach preserves all relevant symmetries of such systems with reversible mode couplings, which establishes the real-time FRG as a valuable tool complementary to classical-statistical simulations. As a first application we show that our approach is consistent with dynamic scaling relations and reproduces the non-trivial value z = d/ 2 for the dynamic critical exponent in d spatial dimensions. Moreover, we extract a novel dynamic scaling function that describes the universal momentum and temperature dependence of the diffusion coefficient of iso-(axial-)vector charge densities in the symmetric phase.