富谷 昭夫

The chiral phase transition in QCD-like theories can be Coleman-Weinberg type supercooling. This is possible to see when Beyond the Standard Model (say, axionlike particle or baryogenesis) is coupled to QCD of the Standard Model (called ordinary QCD). Identifying such a supecooling chiral phase transition thus opens a new window to search for new physics associated with the QCD phase transition epoch of the thermal history, to be probed by gravitational wave and primordial black hole productions. We discuss this possibility by monitoring ordinary QCD setup in a view of a two-flavor Nambu-Jona-Lasinio model in hot and/or dense medium, at the mean-field approximation level. We find that the identification essentially follows the scale violation classification: soft-scale breaking and quantum scale anomaly.

We propose a Transformer neural network architecture specifically designed for lattice QCD, focusing on preserving the fundamental symmetries required in lattice gauge theory. The proposed architecture is gauge covariant/equivariant, ensuring it respects gauge symmetry on the lattice, and is also equivariant under spacetime symmetries such as rotations and translations on the lattice. A key feature of our approach lies in the attention matrix, which forms the core of the Transformer architecture. To preserve symmetries, we define the attention matrix using a Frobenius inner product between link variables and extended staples. This construction ensures that the attention matrix remains invariant under gauge transformations, thereby making the entire Transformer architecture covariant. We evaluated the performance of the gauge covariant Transformer in the context of self-learning HMC. Numerical experiments show that the proposed architecture achieves higher performance compared to the gauge covariant neural networks, demonstrating its potential to improve lattice QCD calculations.

We present our preliminary results on the machine learning estimation of $\text{Tr} \, M^{-n}$ from other observables with the gradient boosting decision tree regression, where $M$ is the Dirac operator. Ordinarily, $\text{Tr} \, M^{-n}$ is obtained by linear CG solver for stochastic sources which needs considerable computational cost. Hence, we explore the possibility of cost reduction on the trace estimation by the adoption of gradient boosting decision tree algorithm. We also discuss effects of bias and its correction.

We present spectral functions extracted from Euclidean-time correlation functions by using sparse modeling. Sparse modeling is a method that solves inverse problems by considering only the sparseness of the solution we seek. To check applicability of the method, we firstly test it with mock data which imitate charmonium correlation functions on a fine lattice. We show that the method can reconstruct the resonance peaks in the spectral functions. Then, we extract charmonium spectral functions from correlation functions obtained from lattice QCD at temperatures below and above the critical temperature $T_{\mathrm{c } }$. We show that this method yields results like those obtained with MEM and other methods.

We develop a new lattice gauge theory code set JuliaQCD using the Julia language. Julia is well-suited for integrating machine learning techniques and enables rapid prototyping and execution of algorithms for four dimensional QCD and other non-Abelian gauge theories. The code leverages LLVM for high-performance execution and supports MPI for parallel computations. Julia's multiple dispatch provides a flexible and intuitive framework for development. The code implements existing algorithms such as Hybrid Monte Carlo (HMC), many color and flavor, supports lattice fermions, smearing techniques, and full QCD simulations. It is designed to run efficiently across various platforms, from laptops to supercomputers, allowing for seamless scalability. The code set is currently available on GitHub https://github.com/JuliaQCD.

We construct an approximate trivializing map by using a Schwinger-Dyson equation. The advantage of this method is that: (1) The basis for the flow kernel can be chosen arbitrarily by hand. (2) It can be applied to the general action of interest. (3) The coefficients in the kernel are determined by lattice estimates of the observables, which does not require analytic calculations beforehand. We perform the HMC with the effective action obtained by the Schwinger-Dyson method, and show that we can have better control of the effective action than the known $t$-expansion construction. However, the algorithmic overhead is still large and overwhelming the gain though faster decorrelation is observed for long-range observables in some cases. This contribution reports the preliminary results of this attempt.

GomalizingFlow.jl: is a package to generate configurations for quantum field theory on the lattice using the flow based sampling algorithm in Julia programming language. This software serves two main purposes: to accelerate research of lattice QCD with machine learning with easy prototyping, and to provide an independent implementation to an existing public Jupyter notebook in Python/PyTorch. GomalizingFlow.jl implements, the flow based sampling algorithm, namely, RealNVP and Metropolis-Hastings test for two dimension and three dimensional scalar field, which can be switched by a parameter file. HMC for that theory also implemented for comparison. This package has Docker image, which reduces effort for environment construction. This code works both on CPU and NVIDIA GPU.

The first-order nature of the chiral phase transition in QCD-like theories can play crucial roles to address a dark side of the Universe, where the created out-of equilibrium is essential to serve as cosmological and astrophysical probes such as gravitational wave productions, which have extensively been explored. This interdisciplinary physics is built based on a widely-accepted conjecture that the thermal chiral phase transition in QCD-like theories with massless (light) three flavors is of first order. We find that such a first order feature may not hold, when ordinary or dark quarks are externally coupled to a weak enough background field of photon or dark photon (which we collectively call a ``magnetic" field). We assume that a weak ``magnetic" background field could be originated from some ``magnetogenesis" in the early Universe. We work on a Nambu-Jona-Lasinio model which can describe the chiral phase transition in a wide class of QCD-like theories. We show that in the case with massless (light) three flavors, the first-order feature goes away when $2 f_\pi^2 \lesssim eB ( \ll (4 \pi f_\pi)^2)$, where $eB$ is the ``magnetic" field strength and $f_\pi$ the pion decay constant at the vacuum. This disappearance is the generic consequence of the presence of the ``magnetically" induced scale anomaly and the ``magnetic" catalysis for the chiral symmetry breaking, and would impact or constrain modeling dark QCD coupled to an external ``magnetic" field.

Violation of the $U(1)$ axial symmetry in QCD is stiffer than the chiral $SU(2)$ breaking, simply because of the presence of the quantum axial anomaly. Hence it might be expected that if and only if the QCD gauge coupling is turned off, or sent to zero (the asymptotic-free limit), where the $U(1)$ axial anomaly goes away, the strength of the $U(1)$ axial breaking trivially coincides with that of the chiral $SU(2)$ breaking. In this write-up, we find that a axial-chiral coincidence occurs even with nonzero QCD gauge coupling, that is a nontrivial coincidence: it is the case with the massive light quarks $(m_l\neq 0)$ and the massless strange quark ($m_s=0$), due to the flavor-singlet nature of the topological susceptibility. This coincidence is robust and tied with the anomalous chiral Ward-Takahashi identity. The nontrivial coincidence implies that the $U(1)$ axial anomaly becomes invisible in the meson susceptibility functions. The invisibility of the $U(1)$ axial anomaly keeps even at hot QCD, so that the chiral $SU(2)$ symmetry restores simultaneously with the $U(1)$ axial symmetry at high temperatures. This simultaneous restoration is independent of the light quark mass, hence is irrespective to the order of the chiral phase transition. We explicitize what the nontrivial coincidence can tell us, by working on a chiral effective model. It turns out that once the strange quark mass gets massive, the topological susceptibility handles the deviation from the nontrivial coincidence. It is then clarified that the large discrepancy between the chiral and axial restorations in the $2+1$ flavors with the physical quark masses is brought by the significant interference of the topological susceptibility. Thus the deviation from the nontrivial coincidence monitored by the topological susceptibility provides a new way of understanding of the chiral and axial breaking in QCD.

We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt $\beta$-VQE to evaluate thermal and quantum expectation values and study the phase diagram for massless Schwinger model along with the temperature and density. By compering the exact variational free energy, we find the variational algorithm work for $T>0$ and $\mu>0$ for the Schwinger model. No significant volume dependence of the variational free energy is observed in $\mu/g \in[0, 1.4]$. We calculate the chiral condensate and take the continuum extrapolation. As a result, we obtain qualitative picture of the phase diagram for massless Schwinger model.

Chiral symmetry is a key to investigating quantum physics, from condensed matter to particle physics. We propose a novel way of realizing a chiral fermion, known as the overlap-Dirac operator, without explicitly calculating the low modes of the Wilson-Dirac operator. We introduce a projection operator inspired by the Sakurai-Sugiura method and formulate the exact sign function and overlap-Dirac operator with a contour-integral form. Like the Sakurai-Sugiura method, the proposing method is multi-scale parallelizable, which fits the multi-core/multi-GPGPU paradigm. We confirm that the quality of chiral symmetry realized with the proposed method is sufficient for double precision. We evaluate the strong scaling of the proposing method.

We find new technical unnaturalness in the standard model, which is a big cancellation between the order parameters for the chiral $SU(2)$ and $U(1)$ axial symmetries related each other at the quantum level of QCD. This unnaturalness can be made technically natural if massless new quarks with a new chiral symmetry is present, which is insensitive to the chiral $SU(2)$ symmetry for the lightest up and down quarks. Thus QCD without such a chiral symmetry is technical unnatural, being shown to be extremely off the defined natural-parameter space. Hypothetical massless quarks might simultaneously solve the strong CP problem, together with the new technical naturalness problem. As one viable candidate, we introduce a dark QCD model with massless new quarks, which can survive current experimental, cosmological, and astrophysical limits, and also leave various phenomenological and cosmological consequences, to be probed in the future. The new unnaturalness can be tested in lattice QCD, gives a new avenue to deeper understand QCD, and provides a new guideline to consider going beyond the standard model.

We find that the chiral phase transition (chiral crossover) in QCD at physical point is triggered by big imbalance among three fundamental quantities essential for the QCD vacuum structure: susceptibility functions for the chiral symmetry, axial symmetry, and the topological charge. The balance, dobbed the QCD trilemma, is unavoidably violated when one of the magnitudes among them is highly dominated, or suppressed. Based on a three-flavor Nambu-Jona-Lasinio model, we explicitly evaluate the amount of violation of the QCD trilemma at physical point, and show that the violation takes place not only at vacuum, but even in a whole temperature regime including the chiral crossover epoch. This work confirms and extends the suggestion recently reported from lattice QCD with 2 flavors on dominance of the axial and topological susceptibilities left in the chiral susceptibility at high temperatures. It turns out that the imbalance is essentially due to the flavor symmetry violation of the lightest three flavors, and the flavor breaking specifically brings enhancement of the axial anomaly contribution in the chiral order parameter, while the the strength of the axial breaking and the transition rate of the topological charge are fairly insensitive to the flavor symmetry. The violation of QCD trilemma and its flavor dependence can be tested by lattice simulations with 2 + 1 flavors in the future, and would also give a new guiding principle to explore the flavor dependence of the chiral phase transition, such as the Columbia plot, including possible extension with external fields.

We propose gauge-covariant neural networks along with a specialized training algorithm for lattice QCD, designed to handle realistic quarks and gluons in four-dimensional space-time. We show that the smearing procedure can be interpreted as an extended version of residual neural networks with fixed parameters. To demonstrate the applicability of our neural networks, we develop a self-learning hybrid Monte Carlo algorithm in the context of two-color QCD, yielding outcomes consistent with those from the conventional Hybrid Monte Carlo approach.

1．はじめに 筆者は2015年に素粒子理論で博士号をとった物理学の研究者であるが，最近は機械学習を理論物理に応用する研究を行っている．機械学習を一言で言えばデータに潜む未知の情報を取り出し運