arXiv subjects

Kiyoharu Kawana

Publications and source records attributed to Kiyoharu Kawana.

At least 19 recordsLinked to original sources

arXiv2026

Loop expansion in polymer field theory: application to phase separation

Liquid-liquid phase separation underlies phenomena ranging from protein condensate formation to the phase coexistence of synthetic polymers. Although the random phase approximation (RPA) is widely used to predict such phase behavior, its quantitative accuracy for binodals of polymer solutions, particularly outside the high-density regime, remains incompletely characterized. Here, we develop a field-theoretic loop expansion in homopolymer systems by identifying the inverse polymer density $ρ^{-1}$ as the Planck constant $\hbar$ in quantum field theory. We calculate the leading-order and next-to-leading-order corrections to the RPA free energy, denoted as RPA+ and RPA++, respectively. Testing the binodal predicted by the RPA+ against molecular dynamics simulations of bead-spring chains with Gaussian pair interactions, we find that the RPA+ qualitatively improves the dilute-phase coexistence density over the RPA, while the critical point error remains comparable to that of the RPA. Our results establish the loop expansion as a systematic route for refining the RPA-based binodal predictions for polymer phase separation.

cond-mat.soft↗

arXiv2026

Revisiting wormhole-induced global symmetry breaking

It is widely believed that global symmetries cannot exist in a consistent theory of quantum gravity. A prominent mechanism underlying this expectation is provided by gravitational instantons or Euclidean wormholes, whose contributions to the Euclidean path integral generates local symmetry-breaking operators in the effective action with couplings parametrized by the $α$-parameters $\overrightarrowα=(α_1^{},α_2^{},\cdots)$. The appearance of these $α$-parameters is often taken as evidence that wormholes explicitly break global symmetries. In this paper, we argue that this conclusion is premature. The fate of the symmetry is determined by the ensemble average over these $α$-parameters. We show that, under broad situations, this average can be sharply dominated by the symmetric point $\overrightarrowα=0$, while contributions from other symmetry-breaking critical points $\overrightarrowα\neq 0$ are typically suppressed by a doubly exponential factor $\exp(-e^{2S_{\rm ins}})$, where $S_{\rm ins}$ is the instanton action. In particular, standard $\mathrm{U}(1)^{}$ Peccei--Quinn models fall into this class, implying that the conventional axion quality problem does not arise in the wormhole-induced effective theory. Our analysis is formulated for general $\mathrm{U}(1)^{}$ $p$-form global symmetries.

hep-th↗

arXiv2026

Variational Method for Interacting Surfaces with Higher-Form Global Symmetries

We develop a variational method for interacting surface systems with higher-form global symmetries. As a natural extension of the conventional second-quantized Hamiltonian of interacting bosons, we explicitly construct a second-quantized Hamiltonian formulated in terms of a closed surface operator $\hatϕ[C_p^{}]$ charged under a $p$-form global symmetry. Applying the variational principle, we derive a functional Schrödinger equation analogous to the Gross-Pitaevskii equation in conventional bosonic systems. In the absence of external forces, the variational equation admits a uniform solution that is uniquely determined by a microscopic interaction potential $U(ψ^*ψ)$ and the chemical potential. This uniform solution describes a uniform gas of bosonic surfaces. Using the obtained energy functional, we show that low-energy fluctuations contain a gapless $p$-form field $A_p^{}$ when the $p$-form global symmetry is $\mathrm{U}(1)$, whereas the $p$-form field becomes massive for discrete symmetries, whose low-energy limit is described by a $\mathrm{BF}$-type topological field theory. As a consequence, the system exhibits abelian topological order with anyonic surface excitations. In the presence of external forces, however, solving the functional equation in full generality remains challenging. We argue, however, that the problem reduces to solving the conventional Gross-Pitaevskii equation when external forces act separately on the center-of-mass and relative motions. In addition, we present analytic solutions for topological defects as analogs of vortex and domain-wall solutions in conventional bosonic systems. Finally, as a concrete microscopic model, we study a $\mathbb{Z}_N^{}$ lattice gauge theory and apply our variational method to this system.

cond-mat.stat-mech↗

arXiv2025

Landau theory for lattice higher gauge theory and Kramers-Wannier duality

We derive a Landau field theory for a lattice higher gauge theory defined on $p$-dimensional open cells (i.e., sites, links, faces, cubes, etc.), and study its continuum-limit and phases. In this approach, the $p$-dimensional Wilson-surface operator of the higher gauge theory is promoted to a fundamental functional field that is charged under the $p$-form global symmetry. By explicitly solving the functional equation of motion, we show that the classical solution exhibits the area~(perimeter) law in the strong (weak) gauge coupling limit. In the deconfined phase, we also construct topological defects for both $\mathrm{U}(1)$ and $\mathbb{Z}_N^{}$ higher gauge theories, as analogs of vortex and domain-wall solutions in conventional field theories with $0$-form global symmetries. Besides, we examine low-energy effective theory by identifying the phase modulations of the functional field as low-energy modes, and discuss the Coleman-Mermin-Wagner theorem for higher-form global symmetries. Finally, we discuss infrared duality among Landau field theories, which originates from Kramers-Wannier duality in lattice higher gauge theories.

hep-th↗

arXiv2025

Classical Continuum Limit of the String Field Theory Dual to Lattice Gauge Theory

We discuss the classical continuum limit of the string field theory dual to the $\mathrm{SU}(N)$ lattice gauge theory and investigate various fundamental phenomena in the continuum theory at the mean-field level. Our construction of the continuum theory is based on the concept of {\it area derivative}, which can be regarded as a generalization of the ordinary derivative $\partial/\partial x^μ$ to operators acting on functional fields $ϕ[C]$ on the loop space. The resultant continuum theory has a $\mathbb{Z}_N^{}$ $1$-form global symmetry, which originates in the $\mathbb{Z}_N^{}$ center symmetry in the gauge theory. We find that the confined and deconfined phases of the gauge theory are identified by the unbroken and broken phases of the $\mathbb{Z}_N^{}$ symmetry respectively by showing the Area/Perimeter law of the classical solution. In the broken phase, the low-energy effective theory is described by a $\mathrm{BF}$-type topological field theory and has a emergent $\mathbb{Z}_N^{}$ $(D-2)$-form global symmetry. The existence of the emergent symmetry is deeply related to $(D-2)$-dimensional topological configurations (i.e. center vortex for $D=4$), and we explicitly construct such a topological defect in the continuum theory. Finally, we also comment on the upper and lower critical dimensions of the gauge theory/string field theory.

hep-th↗

arXiv2025

Phases and propagation of closed p-brane

We study phases and propagation of closed $p$-brane within the framework of effective field theory with higher-form global symmetries, i.e., {\it brane-field theory}. We extend our previous studies by including the kinetic term of the center-of-mass motion as well as the kinetic term for the relative motions constructed by the area derivatives. This inclusion gives rise to another scalar Nambu-Goldstone mode in the broken phase, enriching the phase structures of $p$-brane. For example, when the higher-form global symmetries are discrete ones, we show that the low-energy effective theory in the broken phase is described by a topological field theory of the axion $φ(X)$ and $p$-form field $A_p^{}(X)$ with multiple (emergent) higher-form global symmetries. After the mean-field analysis, we investigate the propagation of $p$-brane in the present framework. We find the (functional) plane-wave solutions for the kinetic terms and derive a path-integral representation of the brane propagator. This representation motivates us to study the brane propagation within the Born-Oppenheimer approximation, where the volume of $p$-brane is treated as constant. In the volume-less limit (i.e. point-particle limit), the propagator reduces to the ordinary propagator of relativistic particle, whereas it describes the propagation of the area elements in the large-volume limit. Correspondingly, it is shown that the Hausdorff dimension of $p$-brane varies from $2$ to $2(p+1)$ as we increase the $p$-brane volume within the Born-Oppenheimer approximation. Although these results are quite intriguing, we also point out that the Born-Oppenheimer approximation is invalid in the point-particle limit, highlighting the quantum nature of $p$-brane as an extended object in spacetime.

hep-th↗

arXiv2025

On Virial Expansion in Hard Sphere Model

Virial expansion is a traditional approach in statistical mechanics that expresses thermodynamic quantities, such as pressure $p$, as power series of density or chemical potential. Its radius of convergence can serve as a potential indicator of phase transition. In this study, we investigate the virial expansion of the hard-sphere model, using the known dimensionless virial coefficients $\tilde{B}_k^{}~(k=1,2,\cdots)$ up to the $12$th order. We find that it is well fitted by $\tilde{B}_k^{}=1.28\times k^{1.90}$, corresponding to the analytic continuation of the virial expansion of the pressure as $\sim \mathrm{Li}_{-1.90}^{}(η)$, where $η$ is the packing fraction and $\mathrm{Li}_s^{}(x)$ is the polylogarithm function. This implies the absence of singular behavior in the physical parameter space $η\leq η_{\mathrm{max}}^{}\approx 0.74$ and no indication of phase transition in the virial expansion approach. In addition, we calculate the cluster-integral coefficients $\{b_l^{}\}_{l=1}^\infty$ and observe that their asymptotic behavior resembles the results obtained in the large dimension limit ($D\rightarrow \infty$), suggesting that $D=3$ might be already regarded as large dimension. However, the existence of phase transition in the hard-sphere model has been confirmed by numerous simulations, which clearly indicates that a naive extrapolation of the virial series can lead to unphysical results.

cond-mat.stat-mech↗

arXiv2025

Geometric conservation in curved spacetime and entropy

We provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge become geometric under a certain initial condition of the scalar function, and show that such a conserved geometric current generally exists in curved spacetime. Furthermore, we demonstrate that the geometric conserved current agrees with the entropy current in an effective theory of a perfect fluid, thus the conserved charge is the total entropy of the system. While the geometric charge can be regarded as the entropy for a nondissipative fluid, its physical meaning should be investigated for more general cases.

hep-th↗

arXiv2024

AdS/CFT correspondence for the $O(N)$ invariant critical $φ^4$ model in 3-dimensions by the conformal smearing

We investigate a structure of a 4-dimensional bulk space constructed from the $O(N)$ invariant critical $φ^4$ model in 3-dimension using the conformal smearing. We calculate a bulk metric corresponding to the information metric and the bulk-to-boundary propagator for a composite scalar field $φ^2$ in the large $N$ expansion. We show that the bulk metric describes an asymptotic AdS space at both UV (near boundary) and IR (deep in the bulk) limits, which correspond to the asymptotic free UV fixed point and the Wilson-Fisher IR fixed point of the 3-dimensional $φ^4$ model, respectively. The bulk-to-boundary scalar propagator, on the other hand, encodes $Δ_{φ^2}$ (the conformal dimension of $φ^2$) into its $z$ (a coordinate in the extra direction of the AdS space) dependence. Namely it correctly reproduces not only $Δ_{φ^2}=1$ at UV fixed point but also $Δ_{φ^2}=2$ at the IR fixed point for the boundary theory. Moreover, we confirm consistency with the GKP-Witten relation in the interacting theory that the coefficient of the $z^{Δ_{φ^2}}$ term in $z\to 0$ limit agrees exactly with the two-point function of $φ^2$ including an effect of the $φ^4$ interaction. }

hep-th↗

arXiv2024

Q-Balls in the presence of attractive force

Q-balls are non-topological solitons in field theories whose stability is typically guaranteed by the existence of a global conserved charge. A classic realization is the Friedberg-Lee-Sirlin (FLS) Q-ball in a two-scalar system where a real scalar $χ$ triggers symmetry breaking and confines a complex scalar $Φ$ with a global $U(1)$ symmetry. A quartic interaction $κχ^2|Φ|^2$ with $κ>0$ is usually considered to produce a nontrivial Q-ball configuration, and this repulsive force contributes to its stability. On the other hand, the attractive cubic interaction $Λχ|Φ|^2$ is generally allowed in a renormalizable theory and could induce an instability. In this paper, we study the behavior of the Q-ball under the influence of this attractive force which has been overlooked. We find approximate Q-ball solutions in the limit of weak and moderate force couplings using the thin-wall and thick-wall approximations respectively. Our analytical results are consistent with numerical simulations and predict the parameter dependencies of the maximum charge. A crucial difference with the ordinary FLS Q-ball is the existence of the maximum charge beyond which the Q-ball solution is classically unstable. Such a limitation of the charge fundamentally affects Q-ball formation in the early Universe and could plausibly lead to the formation of primordial black holes.

hep-ph↗

arXiv2024

Field Theory for Superconducting Branes and Generalized Particle-Vortex Duality

We propose a field theory of closed $p$-brane $C_p^{}$ interacting with a $(p+1)$-form gauge field $A_{p+1}^{}$. This is a generalization of the Ginzburg-Landau theory (Abelian-Higgs model) for superconducting particles to higher-dimensional superconducting branes. A higher-form gauge invariant action is constructed by utilizing the Area derivative, which is a higher-dimensional generalization of the ordinary derivative. We find that the fundamental phenomena of superconductivity, such as the Meisser effect, topological defects, topological order, are naturally extended in the brane-field theory. We explicitly construct a topologically non-trivial static configuration that is characterized by the first homotopy group. Then, we calculate the low-energy effective theory in the presence of the topological defect and find that it is described by a BF-type topological field theory coupled with the world-volume of the topological defect. We also conjecture an infra-red duality between the superconducting brane-field model and dual brane-field model with a global $\mathrm{U}(1)$ higher-form symmetry as a generalization of the Particle-Vortex duality.

hep-th↗

arXiv2024

Higgs Alignment from Multicritical-Point Principle in Two Higgs Doublet Models

In models with non-minimal Higgs sectors, enforcing (near) Higgs alignment, necessary to prevent significant deviations in the Higgs boson coupling from the standard model prediction, causes a serious fine-tuning problem. We demonstrate that the Higgs alignment is naturally deduced from the multicritical point principle (MPP) in the general two Higgs doublet model. Furthermore, we discuss the possibility of realizing the Yukawa alignment from the MPP, which is necessary to prevent flavor-changing neutral currents mediated by Higgs bosons at tree level.

hep-ph↗

arXiv2023

PBH formation from overdensities in delayed vacuum transitions

Primordial black hole (PBH) formation from first-order phase transitions (FOPTs) combines two prevalent elements of beyond the Standard Model physics with wide-ranging consequences. We elaborate on a recently proposed scenario in which inhomogeneities in vacuum energy decay seed the overdensities that collapse to PBHs. In this scenario, the PBH mass is determined by the Hubble mass as in conventional formation scenarios, while its number density is determined by the nucleation dynamics of the FOPT. We present a detailed study of the formation probability including parameter dependencies. In addition, we generate populations in the open mass window as well as for the HSC and OGLE candidate microlensing events. This mechanism inevitably creates PBHs in generic FOPTs, with significant populations produced in slow and moderately strong phase transitions.

astro-ph.CO↗

arXiv2023

Effective Brane Field Theory with Higher-form Symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for $p$-dimensional objects. In the case of a $p$-form symmetry, the fundamental field $ψ[C_p^{}]$ is a functional of $p$-dimensional closed brane $C_p^{}$ embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of $\mathrm{U}(1)$ $p$-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of $C_p^{}$. In the latter case, the low-energy effective theory is described by the $p$-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

hep-th↗

arXiv2023

Note on general functional flows in equilibrium systems

We study the response of generating functionals to a variation of parameters (couplings) in equilibrium systems i.e. in quantum field theory (QFT) and equilibrium statistical mechanics. These parameters can be either physical ones such as coupling constants or artificial ones which are intentionally introduced such as the renormalization scale in field theories. We first derive general functional flow equations for the generating functional (grand-canonical potential) $W[J]$ of the connected diagrams. Then, we obtain functional flow equations for the one-particle irreducible ($1$PI) vertex functional (canonical potential) $Γ[ϕ]$ by performing the Legendre transformation. By taking the functional derivatives of the flow equations, we can obtain an infinite hierarchical equations for the $1$PI vertices. We also point out that a Callan-Symanzik type equation holds among the vertices when partition function is invariant under some changes of the parameters. After discussing general aspects of parameter response, we apply our formalism to several examples and reproduce the well-known functional flow equations. Our response theory provides us a systematic and general way to obtain various functional flow equations in equilibrium systems.

cond-mat.stat-mech↗

arXiv2023

Bulk modified gravity from a thermal CFT by the conformal flow

We construct a bulk spacetime from a boundary CFT, $O(N)$ free scalar model, at finite temperature using a smearing technique, called a conformal flow. The bulk metric is constructed as an information metric associated with the boundary thermal state. Near the boundary (UV region), an asymptotically AdS spacetime is obtained with a leading order perturbation of scalar mode. Based on the falloff behavior of the perturbations and the $O(N)$ symmetry in the CFT, we argue that the corresponding bulk theory is a modified gravity with scalar mode such as $f(R)$ gravity rather than Einstein's general relativity coupled minimally to matter fields. Moving to Einstein frame, we show that the metric is asymptotically the same as the AdS black brane solution. On the other hand, deep in the bulk (IR region), the spacetime turns out to be conformally equivalent to the near horizon limit of AdS extremal black brane, though it is no longer a solution of $f(R)$ gravity, and hence more general classes of modified gravity need to be considered.

hep-th↗

arXiv2023

Quantum phase transition and absence of quadratic divergence in generalized quantum field theories

In ordinary thermodynamics, around first-order phase transitions, the intensive parameters such as temperature and pressure are automatically fixed to the phase transition point when one controls the extensive parameters such as total volume and total energy. From the microscopic point of view, the extensive parameters are more fundamental than the intensive parameters. Analogously, in conventional quantum field theory (QFT), coupling constants (including masses) in the path integral correspond to intensive parameters in the partition function of the canonical formulation. Therefore, it is natural to expect that in a more fundamental formulation of QFT, coupling constants are dynamically fixed a posteriori, just as the intensive parameter in the micro-canonical formulation. Here, we demonstrate that the automatic tuning of the coupling constants is realized at a quantum-phase-transition point at zero temperature, even when the transition is of higher order, due to the Lorentzian nature of the path integral. This naturally provides a basic foundation for the multi-critical point principle. As a concrete toy model for solving the Higgs hierarchy problem, we study how the mass parameter is fixed in the $ϕ^4$ theory at the one-loop level in the micro-canonical or further generalized formulation of QFT. We find that there are two critical points for the renormalized mass: zero and of the order of ultraviolet-cutoff. In the former, the Higgs mass is automatically tuned to be zero and thus its fine-tuning problem is solved. We also show that the quadratic divergence is absent in a more realistic two-scalar model that realizes the dimensional transmutation. Additionally, we explore the possibility of fixing quartic coupling in $ϕ^4$ theory and find that it can be fixed to a finite value.

hep-th↗

arXiv2023

Entropy and its conservation in expanding Universe

We investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding Universe. We show that the conserved charge in the inflation era becomes the Bekenstein-Hawking entropy for de Sitter space, and it becomes the matter entropy and the radiation entropy in the matter and radiation dominated eras, respectively, while the charge itself is always conserved. These properties are qualitatively confirmed by a numerical analysis of a model with a scalar field and radiations. Results in this paper provide more evidences on the interpretation that the conserved charge in general relativity corresponds to entropy.

hep-th↗