Gergely Fejős (Eötvös Loránd University): "Continuous Chiral Phase Transitions and the Role of the Axial Anomaly"
TBA
Masatoshi Yamada (Kwansei Gakuin University): "The θ-vacuum from functional renormalisation"
We study topological properties of a quantum mechanical system with U(1)-symmetry within the functional renormalisation group (fRG) approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically we embed the original symmetry into the complex plane, U(1)→ℂ. We compute the effective potential of a given topological sector by restricting ourselves to field configurations with a given generalised non-trivial Chern-Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schrödinger equation.
Shunsuke Yabunaka (JAEA): "Spontaneous breaking of scale invariance at the tricritical FP in the O(N) model at $N=\infty$ and d=3"
TBA
Takeru Yokota (Osaka Institute of Technology): "Neural network solver for functional differential equations and application to FRG"
Although the formulation of the FRG is exact, in practice calculations must be performed approximately. The reason is that solvers for functional differential equations (FDEs), such as the Wetterich equation, have not yet been established. Meanwhile, physics-informed neural networks (PINNs) have recently attracted attention as an efficient method for solving high-dimensional partial differential equations. Since FDEs are essentially high-dimensional differential equations, PINNs are expected to serve as useful solvers for FRG. In this talk, I will discuss the application of PINNs to FRG. In particular, I will present applications to toy models and address the challenges that arise. In our approach, the effective action is represented by a network, and I discuss network architectures that are useful for ensuring convexity—important for the description of phase transitions—as well as for improving interpretability of the results. This talk is based on Refs. [1,2].
[1] T. Yokota, Physics-informed neural networks for solving functional renormalization group on a lattice, Phys. Rev. B 109, 214205 (2024).
[2] T. Miyagawa and T. Yokota, Physics-informed neural networks for functional differential equations: cylindrical approximation and its convergence guarantees, NeurIPS2024 (2024).
Daiki Suenaga (Nagoya University): "Linear sigma model studies in two-color QCD with FRG method"
Two-color QCD (QC2D) serves as a useful testing ground to take a closer look at color-singlet diquark nature as well as to explore cold-dense QCD medium thanks to sign-problem-free lattice simulations. In this talk I will introduce our linear sigma model (LSM) which is capable of explaining low-lying mesons and diquarks measured on the lattice in QC2D. Then, I will show our recent results on fate of the U(1) axial anomaly effects focusing on roles of the diquarks and possible phase transition scenarios at finite temperature, from FRG method in our QC2D LSM. Finally I will present potential future directions of the LSM study in QC2D.
Álvaro Pastor Gutiérrez (RIKEN iTHEMS): "Dynamical symmetry breaking in chiral gauge theories and first steps towards their IR phases"
I will discuss dynamical symmetry breaking in a class of chiral gauge theories that includes the Georgi–Glashow model originally proposed for GUT extensions of the Standard Model. These theories contain a gauge sector and two fermion species transforming in the two-index antisymmetric and antifundamental representations, with different multiplicities, and remain largely inaccessible. Using the effective action formalism and the non-perturbative functional renormalization group, we derive the flows of four-fermion interactions, which capture resonant structures and provide information about bound-state formation. Extending the setup to multiple generations, we connect to the loss of asymptotic freedom and explore the boundary of a conjectured conformal window. Our results show that, while most of theory space favors a dominant color-breaking condensate, there exists a strongly coupled regime where the leading condensation channels fail and more intricate dynamics are expected. Finally, I will outline first steps towards describing the deep IR of these theories using scale-dependent field redefinitions and incorporating color confinement. This talk is based on 2507.21208 and 2412.12254.
Fumio Terazaki (Tokyo University of Science): "Functional renormalization group analysis of relativistic Bose-Einstein condensation"
We perform a non-perturbative analysis of a relativistic complex scalar field theory using the functional renormalization group (FRG). In this theory, it is known that the flow equation of the effective potential becomes complex in the Bose–Einstein condensed phase, which makes it impossible to calculate the condensate. In this talk, we propose an FRG approach that avoids this problem by introducing a new condition. Furthermore, we show that quantum fluctuations induce a significant shift of the critical point in the strong-coupling regime, and that the Mermin–Wagner theorem, which applies to finite-temperature and low-dimensional systems, also holds at finite chemical potential in the theory.
