Searcharxiv⌕ Search

arXiv subjects

Takeshi Fukuyama

Publications and source records attributed to Takeshi Fukuyama.

At least 19 recordsLinked to original sources
arXiv2026

Updated analysis of minimal supersymmetric SO(10) with a universal soft spectrum

We update the analysis of minimal supersymmetric $\SO{10}$ grand unification with a universal, constrained-MSSM-like soft-breaking spectrum. A pair of Yukawa matrices in the $\rep{10}\oplus\overline{\rep{126}}$ Higgs sector fixes the charged fermion masses and quark mixing, the baryon number-violating dimension-five operators that mediate proton decay, and the right-handed neutrino Majorana masses of the type-I seesaw. The simultaneously imposed constraints include: (i) gauge coupling unification and vacuum stability; (ii) dimension-five proton decay (the dimension-six gauge mode also computed and negligible), the $125$-GeV Higgs mass, and the Large Electron-Positron Collider (LEP) chargino limit; and (iii) $μ\to eγ$, the muon $g-2$, and electric dipole moments. We perform a global scan over the soft-breaking parameters, complemented by a constrained-$μ$ cross-check that fixes the electroweakino sector from the GUT-scale boundary conditions through radiative electroweak symmetry breaking. Subject to a single effective colored Higgs scale $\MHC$ for the proton decay normalization (common to unification and decay, though in a general color triplet mass matrix the two can differ) and to a constrained-$μ$ treatment, what survives is a narrow mini-split region: heavy, multi-tens-of-TeV scalars with $\mzero \gtrsim 11.0$~TeV for a dressing electroweakino mass $m_χ=1$~TeV and $\tb \lesssim 8.0^{+5.5}_{-2.0}$, the uncertainty being the Higgs mass theory error. We also examine the fate of the lightest supersymmetric particle as a dark matter candidate, in both the universal model and its free-$μ$ non-universal-Higgs-mass extension. The surviving region is sharply bounded and testable in the coming decade, most directly by Hyper-Kamiokande proton decay and electroweakino searches, with dark matter direct detection and electric dipole moment experiments.

hep-ph↗
arXiv2026

The Nakamura Conjecture Revisited: Toda Molecules and Stationary Axisymmetric Gravity

We revisit the Nakamura conjecture, which relates the Tomimatsu-Sato solutions of stationary axisymmetric gravity to finite Toda molecules. While the conjecture has been established partially, its general rotating sector remains an open problem. We show that the Toda determinants underlying the conjecture possess a natural weight grading. In particular, the two functions entering the Ernst potential have weights n^2 and n^2-1, and this grading extends systematically to shifted determinants labelled by partitions. In coordinates adapted to the Toda generators, each differentiation corresponds to adding one box to the associated Young diagram and increases the weight by one. The same integer n^2 also appears in the zero-order term of the Nakamura bilinear operator, revealing a compatibility between the differential equation and the determinant grading. The partition structure further explains the previously unresolved behavior of second derivatives. Repeated differentiation in one direction produces an internal sector and an external sector requiring only a one-step extension of the Wronskian hierarchy; the latter is reduced by a local three-term Pluecker relation. Thus weight grading, Young-diagram growth, Wronskian enlargement, and Pluecker reduction emerge as parts of a single determinant structure. The unit weight relation n^2 = (n^2-1) + 1 also singles out the elementary Toda seed as a natural third object, suggesting a possible route toward a genuine trilinear formulation. Although no trilinear closure is assumed here, the present construction reduces the remaining general-n Nakamura problem to definite determinant-minor identities and provides a structural framework in which such a formulation can be investigated.

nlin.SI↗
arXiv2026

Detector Resolution and Observable Infrared Memory in QED

Infrared divergences in QED cancel in inclusive observables through the Bloch--Nordsieck and KLN mechanisms. However, this cancellation removes only the unphysical infrared regulator. The detector resolution scale $ω_{\max}$, which specifies the maximum energy of unresolved soft photons, remains in the observable cross section. We emphasize that this surviving scale has a natural interpretation as a coarse-graining scale in the reduced density matrix of the hard sector. Soft photons below $ω_{\max}$ are not observed and are effectively traced over. The corresponding soft-sector overlap therefore becomes resolution dependent, $D_{ij}=D_{ij}(ω_{\max})$. Observable infrared memory is consequently defined not only by the asymptotic soft sector itself, but also by the resolution scale separating observed and unobserved infrared degrees of freedom. This provides a bridge between the traditional infrared-safe cross-section formulation and the modern interpretation of soft photons as carriers of infrared memory and quantum information.

hep-ph↗
arXiv2026

Toward a Unified Axion Cosmology

We explore a unified axion framework connecting grand unification, string-inspired axion-like particles (ALPs), and cosmology. Starting from the QCD axion associated with Peccei--Quinn symmetry in supersymmetric SO(10) GUT, we consider the broader spectrum of ultralight ALPs motivated by heterotic string theory. Within this multi-axion structure, we focus on two ultralight scales selected by cosmological requirements. A mode of order $10^{-22}$ eV is assumed to constitute the dominant dark-matter component and can form a Bose--Einstein condensate whose attractive self-interaction leads to nonlinear collapse, providing possible seeds for high-redshift supermassive black holes. A lighter eigen-direction with a characteristic dynamical scale of order $10^{-28}$ eV can transiently increase the pre-recombination expansion rate and reduce the sound horizon. An order-of-magnitude estimate shows that addressing the Hubble tension requires a sound-horizon-weighted axion fraction of order 0.1, corresponding, for a large initial displacement, to an effective decay constant of order $10^{18}$ GeV. We show that a multi-axion--multi-instanton system can in principle provide both the required aligned light direction and a higher-order effective potential that makes the $10^{-28}$ eV contribution transient. The framework links theoretically motivated axionic degrees of freedom to the distinct scales required by dark-matter, early-black-hole, and Hubble-tension phenomenology.

hep-ph↗
arXiv2026

Reduced Trilinear Reformulation of the Nakamura Conjecture

The Tomimatsu--Sato (TS) family, characterized by the rotation parameter $q$ and the TS index $δ=n,$ provides an important class of exact stationary axisymmetric vacuum solutions of Einstein's equations, whose integrable structure is known to be closely related to the $n$-point Toda molecule hierarchy through the Nakamura Conjecture. However, the set of equations appearing in the Nakamura Conjecture contains not only Hirota bilinear derivatives but also ordinary first-derivative terms, and therefore is not formulated entirely within the conventional bilinear algebra. In this paper we introduce a reduced trilinear formulation based on the reduced sector $(a,b,c)\rightarrow(a,b,1)$ of the $Z_3$-symmetric trilinear Hirota operators. We show that both the Hirota bilinear derivatives and the ordinary derivatives appearing in the Nakamura Conjecture can be rewritten completely within this reduced trilinear framework. Consequently, the set of equations admits a formulation in terms of reduced trilinear operators. We further show that the reduced trilinear formulation naturally inherits a Hirota-type direct method. The conventional bilinear spectral factor $k_i-k_j$ is replaced by the $Z_3$-weighted combinations $k_i+ωk_j$ and $k_i+ω^2k_j$, providing a direct-method structure characteristic of the reduced trilinear hierarchy. These results suggest that the Toda-molecule description of the Tomimatsu--Sato hierarchy may be viewed as a reduced sector of a broader trilinear framework, and provide a new perspective on the integrable structure of stationary axisymmetric gravity.

nlin.SI↗
arXiv2026

Gauge Theory of Gravity and the AdS/CFT Correspondence

We discuss the AdS/CFT correspondence from the viewpoint of the gauge-theoretic formulation of gravity, in which gravity is interpreted as a broken phase of conformal gauge symmetry. In the AdS$_2$/CFT$_1$ case, we show that the Schwarzian derivative naturally emerges from the boundary extrinsic curvature of AdS$_2$ geometry. The relation between the bulk Liouville geometry and the boundary projective structure is clarified. We further discuss the distinction between the bulk conformal gauge algebra with vanishing central extension and the emergent boundary Virasoro structure with nonvanishing central charge. We then investigate the possible structure of the AdS$_4$/CFT$_3$ correspondence, which is directly related to the original four-dimensional formulation of gravity as a broken phase of conformal gauge symmetry. In this framework, the Einstein--Hilbert action with cosmological constant emerges together with a total derivative term. We argue that this structure induces the boundary gravitational Chern--Simons term, whose variation leads naturally to the Cotton tensor. The Cotton tensor is interpreted as the fundamental conformal invariant associated with the residual boundary conformal geometry, playing a role analogous to that of the Schwarzian derivative in AdS$_2$/CFT$_1$. We also discuss the qualitative difference between AdS$_4$/CFT$_3$ and AdS$_5$/CFT$_4$. While the former appears naturally connected with gravity arising from conformal symmetry breaking, the latter may require genuinely higher-dimensional, string-inspired structures beyond the four-dimensional conformal gauge framework. These observations suggest a unified geometrical interpretation of holography in terms of boundary remnants of broken conformal gauge symmetry.

hep-th↗
arXiv2026

The General Structure of Trilinear Equations

We investigate trilinear structures as a natural extension of the Hirota bilinear formalism in integrable systems. While bilinear equations are associated with Grassmannian geometry and Plücker relations, trilinear equations suggest a higher algebraic structure involving three-slot couplings of tau functions. Focusing on the stationary axisymmetric Einstein equations, we show that when the Ernst potential is written in a tau-ratio form, the nonlinear equation decomposes into a cubic sector containing all second-derivative terms and a quartic gradient envelope. The cubic sector is identified with a YTSF-type trilinear kernel. We formulate a general trilinear kernel criterion and apply it to the Tomimatsu--Sato solutions. In particular, we demonstrate that the $δ=3$ solution possesses the same trilinear kernel structure as the $δ=2$ case, with a universal normalization up to a constant factor. These results suggest that the trilinear kernel represents a universal structure governing the highest-derivative sector of the Ernst system, providing a new perspective on integrability beyond the bilinear hierarchy.

nlin.SI↗
arXiv2026

Evidence for Log-Periodic Modulation in High-Redshift Compact Object Abundance Consistent with Cyclic Condensate Collapse

We analyze the redshift distribution of high-$z$ galaxies and active galactic nuclei identified in early JWST data, and investigate the presence of periodic structure in the variable $x=\ln(1+z)$. A baseline-corrected unbinned frequency analysis reveals a statistically significant peak corresponding to a spacing $Δx \simeq 0.34$, suggesting an approximately log-periodic pattern in the redshift distribution. A periodic structure in $x$ implies a preferred scaling ratio in $(1+z)$, which may be interpreted as a realization of discrete scale invariance. We discuss the possibility that such behavior arises from cyclic condensate dynamics in Bose--Einstein condensate (BEC) cosmology. In the Fukuyama--Morikawa--Tatekawa framework, repeated collapse and re-formation episodes of a self-interacting condensate occur over characteristic timescales of order several $10^8$ years. When mapped into redshift space, this temporal periodicity naturally translates into an approximately constant spacing in $\ln(1+z)$. While the observed frequency is not interpreted as a sharp theoretical prediction, its magnitude is quantitatively consistent with the intrinsic cycle timescale of QCD-axion motivated condensate dynamics. The present analysis therefore provides observational support for cyclic BEC cosmology as a viable dynamical origin of log-periodic structure in the high-redshift universe.

astro-ph.CO↗
arXiv2026

Infrared Divergence in QED and the Fluctuation of Electromagnetic Fields

We establish a no-go result for the infrared sector of quantum electrodynamics. Using the standard Fock-space formulation, we show that gauge invariance enforces coherent soft-photon phases that guarantee the Bloch--Nordsieck/Kinoshita--Lee--Nauenberg cancellation for all inclusive observables. The infrared divergences of perturbative amplitudes therefore do not signal any physical instability of the theory, but reflect the universal quantum dressing cloud inseparably accompanying charged particles. We further demonstrate that the stochastic interpretation suggested by the Schwinger--Keldysh effective action does not apply to four-dimensional Maxwell theory. Although infrared-sensitive imaginary terms appear in the SK effective action and can be rewritten via a Hubbard--Stratonovich transformation, we prove that conformal invariance forbids any infrared growth of these terms. As a consequence, the associated auxiliary field cannot be interpreted as a Langevin force, even in de~Sitter spacetime. These results exclude infrared-induced classical stochastic dynamics for gauge fields and clarify the physical distinction between QED and nearly massless scalar fields in de~Sitter space.

hep-th↗
arXiv2026

Emergent equilibrium-like yields from nonequilibrium cascade dynamics

We study nonequilibrium cascades in which fragile bound or coherent structures are formed through intermediate states rather than by direct equilibration. Motivated by light-nuclei production in relativistic heavy-ion collisions and by Bose--Einstein condensation in cosmological settings, we analyze such processes within the Schwinger--Keldysh real-time formalism. We show that commonly used rate equations can be understood as a controlled Markovian approximation obtained by integrating out intermediate reservoirs in an underlying multi-component nonequilibrium dynamics. When the finite lifetime of these reservoirs is retained, non-Markovian memory effects naturally appear, leading to delayed and history-dependent formation dynamics. The associated memory time provides a quantitative criterion for the validity of reduced, rate-based descriptions far from equilibrium.

hep-ph↗
arXiv2026

Trilinear Kernel Structure and Its Gravitational Realization

We clarify the structural role of trilinear kernels in multidimensional integrable hierarchies and in stationary axisymmetric gravity. The Yu--Toda--Fukuyama (YTF) trilinear equation of Ref.~\cite{YuTodaSasaFukuyama:1998hierarchy} is shown to represent not a particular evolution equation but a universal kernel that generates the entire $(3+1)$--dimensional hierarchy by selecting commuting flows. The frequently quoted trilinear equation of Ref.~\cite{YTSF1998} is identified as one such flow of this kernel. We further show that stationary axisymmetric gravity corresponds to a projective realization of the YTF kernel rather than to any single flow. Imposing $\GL(2)$ covariance and homogeneity on the kernel leads uniquely to a gravitational trilinear kernel $\mathcal{Y}(τ_0,τ_1)$, whose vanishing reproduces the Ernst equation. The Tomimatsu--Sato family \cite{Tomimatsu1972} and related bilinear solutions are shown to arise as degenerate submanifolds of this projected trilinear structure, in agreement with the multilinear analysis of Ref.~\cite{Fukuyama:2025TS}. These results establish a unified structural framework linking multidimensional trilinear integrability, stationary gravity, and bilinear solution sectors, and clarify why trilinear kernels are both necessary and sufficient for describing soliton dynamics with projective geometry.

gr-qc↗
arXiv2025

Universal Non-Equilibrium Cascade in QGP Light-Nuclei Formation and Cosmological Bose-Einstein Condensation

Recent ALICE results demonstrate that over 90\% of light nuclei and anti-nuclei ($d$, $\bar d$) observed in heavy-ion collisions originate from a non-equilibrium, multi-stage process: $Δ$-resonance production, decay into correlated nucleons, and their subsequent coalescence in a cooler hadronic environment. Although the final particle yields appear thermal, the underlying dynamics is strongly time-ordered and highly non-equilibrium. We show that this mechanism exhibits a striking universality with the formation of Bose-Einstein condensates (BEC) and associated density spikes in cosmological scalar-field dark-matter scenarios. In both systems -- the quark-gluon plasma near hadronization and the early universe approaching the BEC critical temperature -- the relevant degrees of freedom reorganize through a hierarchical cascade: high-energy modes first convert into intermediate excitations, which then seed low-energy coherent structures once the temperature crosses a threshold. This work highlights an unexpected theoretical bridge between heavy-ion physics and cosmology, suggesting a common class of emergent non-equilibrium phenomena behind structure formation in both extremes.

hep-ph↗
arXiv2025

Tau--Function Multilinear Hierarchy of the Tomimatsu--Sato Spacetime: A Gravitational Realization of the YTSF Integrable Structure

The Tomimatsu--Sato (TS) family generalizes the Kerr black hole to higher multipole order $δ$ and has long been regarded as algebraically complicated without any clear integrability. We show instead that stationary axisymmetric vacuum Einstein equations, when the Ernst potential is written as a $τ$--ratio $\mathcal{E}=τ_1/τ_0$, admit a universal decomposition of the Ernst numerator into a cubic part containing all second derivatives and a quartic \emph{gradient envelope}. The cubic sector can be written in terms of $Z_3$--symmetric trilinear Hirota operators, revealing a hidden integrable structure. For $δ=2$, using the explicit Tomimatsu--Sato polynomials, we verify that this trilinear sector coincides with a Yu--Toda--Sasa--Fukuyama (YTSF) equation-type kernel. Thus the TS geometry forms a gravitational realization of a multilinear $τ$--function hierarchy in stationary axisymmetric general relativity.

gr-qc↗
arXiv2025

Axion in the minimal SO(10) GUT

The QCD axion is investigated within the minimal supersymmetric SO(10) grand unified theory, where the Yukawa sector involves Higgs multiplets ${\bf 10}$ and $\overline{\bf 126}$. The relative phase between the VEVs of $({\bf 10,1,3})\subset\overline{\bf 126}$ and $({\bf \overline{10},1,3})\subset{\bf 126}$ under ${\rm SU}(4)_C\times{\rm SU}(2)_L\times{\rm SU}(2)_R$ is identified with the axion. The Peccei-Quinn and $B-L$ symmetry breaking scales coincide through $|\langleΔ_R\rangle|=|\langle\overlineΔ_R\rangle|$. The scalar partner of the lightest right-handed neutrino plays the role of the inflaton, realizing hybrid inflation consistent with the observed CMB density fluctuations. After inflation, both fields acquire VEVs, and the domain-wall problem is resolved through the Lazarides-Shafi mechanism, which naturally restricts the model to three generations.

hep-ph↗
arXiv2025

Bose-Einstein Condensate Cosmology within the Framework of QCD Axion

Bose-Einstein Condensation (BEC) cosmology is analyzed in the framework of a string-inspired axion model. The dispersion relation of the axionic mode includes both gravitational and self-interaction terms, the latter being small in magnitude but crucial for inducing instability of the condensate. The generation rate of BEC around redshift $z\approx 30$ is primarily governed by gravity, consistent with a phenomenological value $Γ\approx 10^{-31}$ eV adopted in previous work and realizable for the QCD axion. The relation between this early BEC epoch and the later formation of supermassive black holes at $z\approx 5$ is also discussed.

hep-ph↗
arXiv2025

The self-attractive ultralight axion and its time scale of collapsing in general relativistic framework

The formation of supermassive black holes (SMBHs) at high red shift $z$ by ultralight axion dark matter (DM) is discussed in the general relativistic framework. The critical condition of collapsing of self-attracting DM in non-relativistic treatment corresponds to dust particle, which allows to estimate the time scale of the SMBH formation and the its length scale in the general relativistic framework. It gives the support of ultralight axion model based on the string model as the origins of the early universe SMBH and the Little Red Dots (LRDs) etc. observed by JWST.

hep-ph↗
arXiv2024

Ultralight axion and modern cosmology tensions

String-inspired axion model is considered to comprehensively solve the problems of modern cosmology, Hubble tension problem, the origin of the stochastic gravitational wave background, and too early formation of supermassive black holes at high $z$.

hep-ph↗