Abstracts

Invited Talks

• Gergely Fejős (Eötvös Loránd University): "Thermal behavior of effective U_A(1) couplings in reflection of higher topological sectors"
  Temperature dependence of the U_A(1) anomaly in the strong interaction remains to be understood around and below the chiral transition. In the framework of the N_f=3 low energy effective meson model, making use the functional renormalization group technique, we derive flow equations for effective, condensate dependent anomaly couplings that arise from instantons with arbitrary winding number of the underlying theory. We provide an approximate numerical solution for this tower of equations, and find that around $T_C$, about 10% of the anomaly arise from the |Q|=2 topological sector. It is also revealed that mesonic fluctuations tend to enhance the anomaly with respect to the temperature, in competition with the exponential suppression of the instanton density at high temperatures.
• Kenji Fukushima (The University of Tokyo): "Dynamical Hadronization and An Application"
  This talk is based on 2103.01129 in collaboration with Jan Pawlowski and Nils Strodthoff. The dynamical hadronization is a general framework for the fRG treatment of bound states. The typical example is found in the problem to describe hadronization out of quarks. The idea of dealing with the composite operators is similar to the Hubbard-Stratonovich transformation in the mean-field level, but the fRG extension called the dynamical hadronization or rebosonization provides us with the flow of the effective degrees of freedom.
• Junichi Haruna (Osaka University): "Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics"
  Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing coarse-graining along the diffusion equations. We apply it for Scalar Quantum Electrodynamics and derive flow equations for the Wilsonian effective action with the perturbative expansion in the gauge coupling. We focus on the quantum corrections to the correlation functions up to the second order of the gauge coupling and discuss the gauge invariance of the GF-ERG flow. We demonstrate that the anomalous dimension of the gauge field agrees with the standard perturbative computation and that the mass of the photon keeps vanishing in general spacetime dimensions. The latter is a noteworthy fact that contrasts with the conventional Exact Renormalization Group formalism in which an artificial photon mass proportional to a cutoff scale is induced. Our results imply that the GF-ERG can give a gauge-invariant renormalization group flow in a non-perturbative way.
• Xu-Guang Huang (Fudan University): "Quark matter under rotation: fRG versus lattice results"
  Due to the recent experimental breakthrough in heavy ion collisions about the spin polarization measurements, the QCD matter under rotation attracts a lot of attentions. It would be quite interesting to ask what would be the effect of a rotation on the QCD phase structure. The natural expectation would be that due to the spin polarization by rotation, all the spin-0 condensate, like the chiral condensate, would be unfavored and thus the chiral phase structure may vary under rotation. We will discuss whether this is the case based on fRG calculation and mean-field calculation in quark-meson model and also based on lattice QCD simulations. We will show the sharp discrepancy between the two and discuss the possible physical reason behind it.
• Katsumi Itoh (Niigata University): "Gauge symmetry and Functional Renormalization Group"
  We consider gauge theory with fRG based on the Batalin-Vilkovisky's antifield formalism. The two key equations are the flow equation and quantum master equation (QME) that guarantees the presence of a gauge symmetry. It will be explained that the two equations are formally compatible. We also show that two equations can be simultaneously solved to give a perturbative action. Based on our perturbative results, we present a gauge-consistent fRG flows for QED with chorally invariant four-fermi interactions.
• Kiyoharu Kawana (Korean Institute for Advanced Study): "General functional flows in equilibrium systems and applications to classical fluid system"
  I will explain how to construct general functional flows in equilibrium systems, which describe the response of the system against the change of parameters (couplings). From this general viewpoint, the ordinary functional renormalization group in QFT can be trivially obtained by taking the (IR) cut-off parameter k as a response parameter. After the general discussion, I will discuss several applications in classical fluid system, i.e. Hierarchical Reference Theory and Density Renormalization Group.
• Kouichi Okunishi (Niigata University): "A statistical mechanics approach to holographic renormalization group"
  We discuss a holographic aspect of the Bethe lattice Ising model, a classical model of the phase transition in statistical mechanics. We analytically formulate a holographic RG for the model and derive the scaling dimensions associated with boundary spins. We also reveal its connection to the p-adic AdS/CFT.
• Shunsuke Yabunaka (JAEA): "The nonperturbative behavior of the tricritical and tetracritical fixed points of the O(N) models at large N"
  We study the Bardeen-Moshe-Bander lines in O (N) model at N=\infty in d=3 and 8/3. The first line in d=3 consists of the tricritical fixed points and ends at the Bardeen-Moshe-Bander fixed point. The large N limit that allows us to find the BMB line must be taken on particular trajectories in the (d, N) plane: d= 3− \alpha /N and not at fixed dimension d= 3. Our study also reveals that the known BMB line is only half of the true line of fixed points, the second half being made of singular fixed points. The potentials of these singular fixed points show a cusp for a finite value of the field and their finite N counterparts a boundary layer. The second line in d=8/3 consists of the tricritical fixed points and ends at the Wison-Fisher fixed point. This seems paradoxical since the stabilities of the Wilson-Fisher fixed point and the tertactical fixed point are different. We show that only their derivatives of the potentials make them different with the subtleties that taking their limit and deriving them do not commute and that two relevant eigenperturbations show singularities at N=\infty. We also discuss the finite-N realization of the second line of FPs in d=8/3.
• Takeru Yokota (RIKEN iTHEMS): "Machine learning to solve functional renormalization group"
  Recent advancements in physics-informed neural network (PINN), a machine-learning framework to solve differential equations, open the possibility of attacking high-dimensional partial differential equations (PDE) numerically. For example, calculations of 10^5-dimensional PDE using PINN have been reported recently. Viewing these developments, I devised FRG-Net, which is a new approach to solving the Wetterich equation, a functional differential equation describing the renormalization group. My idea is based on the combination of the basis function expansion (BFE) and PINN. BEF for the fields transforms the Wetterich equation into a high-dimensional PDE, and PINN makes it possible to perform the calculation with many basis functions. In FRG-Net, the effective action is represented by a neural network (NN). This is expected to provide a flexible and accurate approximation method because of the universal approximation theorem. In addition to the formalism, I will present a numerical demonstration using the zero-dimensional O(N) model to see the accuracy and the scalability with respect to the input dimensions. I will show that the effective action and the self-energy are accurately obtained using FRG-Net at least up to 100-dimensional inputs.