arXiv subjects

Yui Hayashi

Publications and source records attributed to Yui Hayashi.

At least 19 recordsLinked to original sources

arXiv2026

Fractional $θ$-dependence from the sum over all instanton sectors

An instanton carries integer topological charge, seemingly at odds with the multibranched $θ$ dependence of the Yang-Mills vacuum. We show that summing over all instanton sectors resolves this mismatch in self-dual supersymmetric $\mathbb{C}P^{N-1}$ and $\mathrm{SU}(N)$ Yang-Mills theories with a chiral mass, in two and four dimensions. The path integral reduces to a sum of instanton moduli-space volumes, yielding the multibranched vacuum structure. In four dimensions, this extends Nekrasov's instanton counting for Seiberg-Witten theory to a QCD-like theory without scalars.

hep-th↗

arXiv2026

Doubly-periodic instanton via the ADHM method and the self-dual monopole-center vortex chain

Calorons, i.e., instantons on $\mathbb{R}^3\times S^1$, with nontrivial asymptotic holonomy decompose into $N$ fundamental monopole constituents. This suggests that a doubly-periodic Yang--Mills instanton on $\mathbb{R}^2\times T^2$ may admit a description in terms of a periodic array of monopole constituents. Starting from the Atiyah--Drinfeld--Hitchin--Manin (ADHM) construction, we derive the $2$d Abelian Hitchin system with impurities as a dual description of the doubly-periodic instanton. We then give a prescription for reconstructing the instanton from the Green's function of this system, assuming a scaling ansatz for the ultraviolet divergences induced by the delta-function impurities. In the far-field limit with strongly anisotropic torus periods, we extend the analysis of Bruckmann and van Baal for multi-calorons and identify an alternating chain of BPS and Kaluza--Klein (KK) monopole constituents: The monopole-center vortex chain arises from the non-Abelian self-dual field especially when an 't Hooft twist cuts the torus into the $1/N$ fragment.

hep-th↗

arXiv2026

Resolving the Effects of the Mixing Process on Hierarchical Structures in Polymer Nanocomposites by Bayesian Ultra-Small-Angle X-ray Scattering Analysis

Bayesian inference was combined with Unified Fit to resolve the effects of the mixing history on polymer nanocomposites whose ultra-small-angle X-ray scattering profiles are nearly indistinguishable by conventional analysis. Bayesian Unified Fit was applied to comparing the aggregate size, internal mass-fractal structure, and surface roughness for three carbon black--filled ethylene propylene diene copolymer rubber samples prepared by different mixing processes. Whereas conventional Unified Fit reported essentially identical carbon-black dispersions, the radius of gyration, mass fractal dimension, and surface fractal dimension for the three samples all followed the same ordering, which coincides with the reported ordering of the tensile strength and elongation at break and suggests that the inferred aggregate hierarchy is physically meaningful for the macroscopic mechanical response. These results identify the aggregate size as a candidate structural descriptor of rubber reinforcement and provide an uncertainty-aware basis for examining processing--structure--property relationships in polymer nanocomposites.

cond-mat.soft↗

arXiv2026

From Self-Dual to Physical $\mathbb{C}P^{N-1}$: Anomalies, Boundary Stokes Phenomenon, and Global Structure of $θ$-vacua

We introduce a two-coupling generalization of $\mathbb{C}P^{N-1}$ model that continuously interpolates between the self-dual ($ε=0$) and the physical ($ε=g$) theories as a useful nonperturbative tool. At $ε\neq g$, this model possesses a chiral imbalance, which may be viewed as a real topological deformation (imaginary-$θ$). We demonstrate that exact quantum equivalence between first- and second-order formulations strictly requires a topological counterterm sourced by a bosonic chiral anomaly. Solving this deformed theory at large $N$ yields two primary results. First, we analytically determine the nonperturbative vacuum structure of the self-dual theory, a self-dual vacuum with a dynamically generated field-strength condensate. Second, we resolve a fundamental paradox where saddles with $(θ+ 2πn) \sim O(N)$ ($n$ is branch number) spuriously yield lower energy densities than the physical ground state. Because the effective action possesses an essential singularity at $F=0$, we show that the Lefschetz thimble analysis must be generalized to include boundary thimbles. A boundary Stokes phenomenon renders the problematic saddles topologically inactive, fully restoring the validity of the large-$N$ expansion for strongly coupled theories.

hep-th↗

arXiv2026

Deconfinement-Higgs continuity in ${\rm SU(2)}$ adjoint Higgs model at finite temperature

We study the finite-temperature phase structure of the four-dimensional ${\rm SU}(2)$ adjoint Higgs model, focusing on a possible \textit{deconfinement-Higgs continuity}: the conjecture that the high-temperature deconfined phase of Yang-Mills theory and the finite-temperature Higgs phase form a single thermodynamic phase. We first perform a global-symmetry analysis, showing that the Higgs and deconfined regimes are expected to share the same symmetry pattern, which is distinct from that of the confined phase. This suggests deconfinement-Higgs continuity, but does not exclude the possibility that the deconfined phase and the Higgs phase are separated by a phase transition not associated with the global symmetries. We then perform a deformation analysis, which yields an explicit continuous path between the ``deconfined symmetric'' and ``deconfined Higgs'' regions in a reduced three-dimensional lattice model. These results indicate that the Higgs and deconfined regimes can be continuously connected, while the confined phase remains distinct.

hep-th↗

arXiv2026

Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function

We propose the gauge-invariant criteria of center-vortex condensation and monopole condensation using the $\mathbb{Z}_N^{[1]}$-symmetry twisted partition functions: The torus twisted partition function characterizes the center-vortex condensation, and the lens-space twisted partition function characterizes the monopole condensation. To justify our proposal, we study how these twisted partition functions behave in the adjoint Higgs phase and show that their leading nontrivial contributions come from the center vortex and monopole, respectively. Using the techniques of topological field theories, we uncover the relation between the center-vortex and monopole condensations, and in particular, we prove that the gapped phase with the center-vortex condensation necessarily shows the monopole condensation, too. We then study a center-vortex model with monopoles as an illustrative example, and the higher-charge monopole condensation gives an example of the symmetry fractionalization, which goes beyond the conventional Wilson-'t Hooft classification.

hep-th↗

arXiv2026

GPU-Accelerated Sequential Monte Carlo for Bayesian Spectral Analysis

Bayesian spectral deconvolution provides a data-driven framework for mathematical model selection and parameter estimation from spectral data. Although highly versatile, it becomes computationally expensive as the number of model parameters, data points, and candidate models increases, often rendering practical applications infeasible. We propose a GPU-accelerated approach in which a sequential Monte Carlo sampler (SMCS) is run in parallel on a GPU to perform Bayesian model selection of the number of spectral peaks and Bayesian estimation of peak-function parameters. Numerical experiments demonstrate that the GPU-parallelized SMCS achieves speedups exceeding 500x over CPU-parallelized replica exchange Monte Carlo (REMC). The method is validated on artificial data designed to emulate X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) measurements, as well as on real experimental spectra. As measurement techniques such as microscopic spectroscopy and in-situ methods continue to drive rapid growth in the volume of spectral data, the proposed approach offers a practical computational foundation for advanced analysis of individual datasets.

stat.CO↗

arXiv2026

Wilson-'t Hooft classification and the perimeter law for dyonic loops in 3d monopole semiclassics

We investigate the long-distance behavior of dyonic loop operators in 4d $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ using the 3d monopole semiclassics. If we employ the naive definition of the 't Hooft loop in the Abelianized regime, the dyonic loop operators do not admit the well-defined computations within the effective field theory. Moreover, if one forcibly proceeds with the computations of their expectation values, all the dyonic loops turn out to show the area law, which contradicts the prediction of the Wilson-'t Hooft classification. In this paper, we resolve this puzzle by employing the notion of screening for line operators, and we argue that the dyonic loops are screened by a defect known as the twist vortex, which is non-dynamical in the infrared effective theory but is dynamical in the original ultraviolet theory. The dyonic loops properly dressed by twist vortices admit the well-defined computations within the effective field theory, and we reproduce the kinematic prediction of the Wilson-'t~Hooft classification using the $3$d monopole semiclassics. Furthermore, we apply our framework to the thermal deconfined phase to evaluate the dual string tension, elucidating the topological nature of $\mathbb{Z}_N$ domain walls. We confirm that the domain-wall state has the phase transition at $θ=π$ in the thermal deconfined phase despite the fact that the bulk state is smooth there.

hep-th↗

arXiv2025

Center-vortex semiclassics with non-minimal 't Hooft fluxes on $\mathbb{R}^2\times T^2$ and center stabilization at large $N$

We consider the semiclassical description of confinement for $4$d $SU(N)$ Yang-Mills theory on small $\mathbb{R}^2\times T^2$ with non-minimal 't Hooft twist $p$ with $\gcd(N,p)=1$. For this purpose, we construct the self-dual center vortex for non-minimal 't Hooft twists from the Kraan-van Baal-Lee-Lu-Yi (KvBLLY) monopoles by using the $3$d Abelianized description of $SU(N)$ gauge fields on $\mathbb{R}^3\times S^1$ with nontrivial holonomy backgrounds. This construction shows the self-dual vortex has (1) the fractional magnetic charge $q/N$ with $pq=1$ mod $N$, (2) the fractional topological charge $1/N$, and (3) the fractional instanton action $S_{\mathrm{YM}}=8π^2/(Ng^2)$. The confinement vacua for $NLΛ\ll 1$ can be described by the dilute gas approximation of center vortices, and we give the semiclassical formula for the $θ$ dependence and confining string tensions. We apply this result to understand the suitable choice of the twist $p$ for center stabilization at large $N$. In particular, we test the proposal using the Fibonacci sequence, $N=F_{n+2}$ and $p=F_n$, suggested in studies of the twisted Eguchi-Kawai model, from the viewpoint of the $1$-form and $0$-form center symmetries.

hep-th↗

arXiv2025

Fractional instantons in 2d $\mathbb{C}P^{N-1}$ model and 4d Yang-Mills theory with 't Hooft twists

We derive the explicit formula for fractional BPS lumps (or fractional instantons) in the $\mathbb{C}P^{N-1}$ nonlinear sigma model on a two-dimensional torus under various shift-clock twisted boundary conditions. After regularizing the $\mathbb{C}P^{N-1}$ model by an $N$-component Abelian-Higgs model, those twisted boundary conditions introduce nontrivial 't~Hooft fluxes $p/N$ for the $U(1)$ gauge field, and the topological charge becomes fractionalized as $k+p/N\in \mathbb{Z}+p/N$. The moduli space is globally determined as the $\mathbb{C}P^{Nk+p-1}$-fiber bundle on a $2$-torus, which is a Kähler manifold of complex dimension $Nk + p$ as predicted by the index theorem. We present two different parametrizations of the moduli space: one of them immediately identifies the small-lump singularity appearing in the $\mathbb{C}P^{N-1}$ limit, while the other makes the modular invariance manifest. We also discuss the implications of our finding for the $4$d $SU(N)$ Yang-Mills theory on the $4$-torus with 't~Hooft twists. By tuning the aspect ratio of the 4-torus, fractional instantons in the $\mathbb{C}P^{N-1}$ model with a non-Fubini-Study metric are obtained through the dimensional reduction of $4$d Yang-Mills theory, whose moduli space coincides with the one obtained for the standard $\mathbb{C}P^{N-1}$ model as complex manifolds.

hep-th↗

arXiv2025

Monopole-vortex continuity of ${\mathcal N}=1$ super Yang-Mills theory on $\mathbb{R}^2 \times S^1 \times S^1$ with 't Hooft twist

We study ${\mathcal N} = 1$ $SU(N)$ super Yang-Mills (SYM) theory on $\mathbb{R}^2\times (S^1)_3\times (S^1)_4$ with the 't Hooft twist. The theory becomes weakly coupled if the length $L_4$ of $(S^1)_4$ is sufficiently small, $NL_4Λ\ll 1$. We explore the nonperturbative dynamics at the weak-coupling regime by changing the size of $L_3$ and uncover how $3$d monopole/bion-based effective theory for $L_3\gg L_4$ is related to the $2$d vortex-based theory for $L_3\approx L_4$. The highlights of our results are (1) the smooth "weak-weak" continuity of the vacuum structure and gluino condensate during the $3$d-$2$d dimensional reduction, (2) the switching of Wilson loop behavior from the area law in $3$d to the perimeter law in $2$d via a "double-string" picture, (3) the role of mass deformation in breaking discrete chiral symmetry and restoring the area law in $2$d, and (4) the microscopic investigation of bions during the reduction from $3$d to $2$d and the cancellation of the vacuum energy due to the hidden topological angle. We also discuss the generalization of our results for (1)--(3) from $\mathcal{N}=1$ SYM to QCD with adjoint quarks.

hep-th↗

arXiv2025

Bayesian Inference for Small-Angle Scattering Data II: Core-Shell Samples

Small-angle scattering (SAS) techniques, which utilize neutrons and X-rays, are employed in various scientific fields, including materials science, biochemistry, and polymer physics. During the analysis of SAS data, model parameters that contain information about the sample are estimated by fitting the observational data to a model of sample. Previous research has demonstrated the effectiveness of Bayesian inference in analyzing SAS data using a sphere model. However, compared with the sphere model, the core-shell model, which represents functional nanoparticles, offers higher application potential and greater analytical value. Therefore, in this study, we propose an analytical method for the more complex and practical core-shell model based on Bayesian inference. Through numerical experiments, we evaluated the performance of this method under different conditions, including measurement times, number of data points, and differences in scattering length density. As a result, we clarify the conditions under which accurate estimations are possible.

physics.app-ph↗

arXiv2024

Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism

Magnetic excitations play a crucial role in understanding the color confinement of $4$d Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of $4$d Yang-Mills theory, we can achieve different weakly-coupled descriptions of confinement phenomena: The monopole mechanism takes place on $\mathbb{R}^3\times S^1$ with the double-trace deformation, and the center-vortex mechanism is effective on $\mathbb{R}^2\times T^2$ with the 't Hooft flux. We unify these two semiclassical descriptions by showing the explicit relation between the monopole and center vortex.

hep-th↗

arXiv2024

Higgs-confinement continuity and matching of Aharonov-Bohm phases

Some gauge theories with a spontaneously broken $U(1)$ symmetry exhibit fractional Aharonov-Bohm (AB) phases around vortices in the Higgs regime. We discuss continuity between confining and Higgs regimes in such gauge theories with fundamental matter fields, focusing on the AB phases. By explicit calculations in relevant lattice models, we demonstrate that the AB phase is smoothly connected between the confining and Higgs regimes, supporting the Higgs-confinement continuity. This result provides new insight into phase structures of gauge theories with superfluidity, such as dense QCD.

hep-th↗

arXiv2024

Non-supersymmetric duality cascade of QCD(BF) via semiclassics on $\mathbb{R}^2\times T^2$ with the baryon-'t Hooft flux

We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the $4$d $SU(N_1) \times SU(N_2)$ gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on $\mathbb{R}^2\times T^2$ with the baryon-'t Hooft flux to obtain the concrete dynamics. The $2$d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determining the phase diagram of the model under the assumption of adiabatic continuity. As an application, we justify the non-supersymmetric duality cascade between different QCD(BF), which has been conjectured in the large-${N}$ argument. Combined with the semiclassics and the large-$N_{1,2}$ limit, we construct the explicit duality map from the parent theory, $SU(N_1) \times SU(N_2)$ QCD(BF), to the daughter theory, $SU(N_1) \times SU(N_2-N_1)$ QCD(BF), including the correspondence of the coupling constants. We numerically examine the validity of the duality also for finite $N_{1,2}$ within our semiclassics, finding a remarkable agreement of the phase diagrams between the parent and daughter sides.

hep-th↗

arXiv2024

Semiclassical analysis of the bifundamental QCD on $\mathbb{R}^2\times T^2$ with 't Hooft flux

We study the phase structure of bifundamental quantum chromodynamics (QCD(BF)), which is the $4$-dimensional $SU(N) \times SU(N)$ gauge theory coupled with the bifundamental fermion. Firstly, we refine constraints on its phase diagram from 't Hooft anomalies and global inconsistencies, and we find more severe constraints than those in previous literature about QCD(BF). Secondly, we employ the recently-proposed semiclassical approach for confining vacua to investigate this model concretely, and this is made possible via anomaly-preserving $T^2$ compactification. For sufficiently small $T^2$ with the 't Hooft flux, the dilute gas approximation of center vortices gives reliable semiclassical computations, and we determine the phase diagram as a function of the fermion mass $m$, two strong scales $Λ_{1},Λ_2$, and two vacuum angles, $θ_1, θ_2$. In particular, we find that the QCD(BF) vacuum respects the $\mathbb{Z}_2$ exchange symmetry of two gauge groups. Under the assumption of the adiabatic continuity, our result successfully explains one of the conjectured phase diagrams in the previous literature and also gives positive support for the nonperturbative validity of the large-$N$ orbifold equivalence between QCD(BF) and $\mathcal{N}=1$ $SU(2N)$ supersymmetric Yang-Mills theory. We also comment on problems of domain walls.

hep-th↗

arXiv2024

Semiclassics for the QCD vacuum structure through $T^2$-compactification with the baryon-'t Hooft flux

We study QCD vacuum structure with the topological $θ$ angle using a recently proposed semiclassical approach on $\mathbb{R}^2 \times T^2$ with the 't Hooft and baryon magnetic fluxes. Under the assumption of adiabatic continuity in this setup, the confining vacuum can be described by the dilute gas of center vortices. With this semiclassical approach, we derive the 2d effective description at small $T^2$ and successfully explain the reasonable theta dependence of the QCD vacuum: In the one-flavor QCD at $θ= π$, the $CP$ symmetry is spontaneously broken for quark mass above a critical value and restored for a subcritical mass, while the $CP$ symmetry is always spontaneously broken in the multi-flavor QCD at $θ= π$. From our semiclassical description, we discuss implications to the $4$d chiral Lagrangian and propose how the $η'$ meson should be incorporated in consistent with known global structures: The periodicity of the $η'$ should be extended from the naive one $2π$ to $2πN$. Additionally, we revisit the phase diagram of $N_f = 1+1$ and $N_f = 1+1+1$ QCD on the up and down quark mass plane, confirming and refining the existence of the $CP$-broken Dashen phase.

hep-th↗

arXiv2024

Quantitative Selection of Sample Structures in Small-Angle Scattering Using Bayesian Methods

Small-angle scattering (SAS) is a key experimental technique for analyzing nano-scale structures in various materials.In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting.This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models.We assess the performance of our method through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that our proposed method analysis approach yields highly accurate and interpretable results.We also discuss the ability of our method to analyze a range of mixing ratios and particle size ratios for mixed components, along with its precision in model evaluation by the degree of fitting.Our proposed method effectively facilitates quantitative analysis of nano-scale sample structures in SAS, which has traditionally been challenging, and is expected to significantly contribute to advancements in a wide range of fields.

physics.data-an↗