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Toshiaki Fujimori

Publications and source records attributed to Toshiaki Fujimori.

At least 19 recordsLinked to original sources
arXiv2025

Domain Wall Networks as Skyrmion Crystals in Chiral Magnets

We theoretically investigate the ground states of a chiral magnet with a square anisotropy and show that it supports domain wall networks as stable ground states. A domain wall junction in the domain wall network turns out to be a skyrmion with half topological charge and, therefore, the found domain wall network has a second topological nature, a skyrmion crystal. More specifically, we present a ground-state phase diagram of the chiral magnet with varying anisotropy parameters consisting of skyrmion lattices, chiral soliton lattices, and ferromagnetic states. In the presence of the square anisotropy, the skyrmion crystal forms a domain wall network. The size of domains in the domain wall network is shown to be tunable by an external magnetic field, offering a way to realize experimentally detectable domain wall networks.

cond-mat.mes-hall↗
arXiv2025

Exact-WKB Analysis of Two-level Floquet Systems

We explore the application of the exact Wentzel-Kramers-Brillouin (WKB) analysis to two-level Floquet systems and establish a systematic procedure to calculate the quasi-energy and Floquet effective Hamiltonian. We show that, in the exact-WKB analysis, the quasi-energy and Floquet effective Hamiltonian can be expressed in terms of cycle integrals (Voros symbol), which characterize monodromy matrices for Schrödinger-type differential equations governing two-level Floquet systems. We analytically evaluate the cycle integrals using the low-frequency expansion and derive both perturbative and non-perturbative corrections to the quasi-energy and Floquet effective Hamiltonian. To verify the accuracy of our results, we compare them with numerical calculations and analyze resonant oscillations, which reveal non-perturbative features that cannot be captured by the perturbative expansion.

hep-ph↗
arXiv2023

Moduli Spaces of Instantons in Flag Manifold Sigma Models -- Vortices in Quiver Gauge Theories

In this paper, we discuss lumps (sigma model instantons) in flag manifold sigma models. In particular, we focus on the moduli space of BPS lumps in general Kähler flag manifold sigma models. Such a Kähler flag manifold, which takes the form $\frac{U(n_1+\cdots+ n_{L+1})}{U(n_1) \times \cdots \times U(n_{L+1})}$, can be realized as a vacuum moduli space of a $U(N_1) \times \cdots \times U(N_L)$ quiver gauged linear sigma model. When the gauge coupling constants are finite, the gauged linear sigma model admits BPS vortex configurations, which reduce to BPS lumps in the low energy effective sigma model in the large gauge coupling limit. We derive an ADHM-like quotient construction of the moduli space of BPS vortices and lumps by generalizing the quotient construction in $U(N)$ gauge theories by Hanany and Tong. As an application, we check the dualities of the 2d models by computing the vortex partition functions using the quotient construction.

hep-th↗
arXiv2023

Resurgence in 2-dimensional Yang-Mills and a genus altering deformation

We study resurgence in the context of the partition function of 2-dimensional $SU(N)$ and $U(N)$ Yang-Mills theory on a surface of genus $h$. After discussing the properties of the transseries in the undeformed theory, we add a term to the action to deform the theory. The partition function can still be calculated exactly, and the deformation has the effect of analytically continuing the effective genus parameter in the exact answer to be non-integer. In the deformed theory we find new saddle solutions and study their properties. In this context each saddle contributes an asymptotic series to the transseries which can be analysed using Borel-Ècalle resummation. For specific values of the deformation parameter we find Cheshire cat points where the asymptotic series in the transseries truncate to a few terms. We also find new partial differential equations satisfied by the partition function, and a number of applications of these are explained, including low-order/low-order resurgence.

hep-th↗
arXiv2022

All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability

We discuss all-order transseries in one of the simplest quantum mechanical systems: a U(1) symmetric single-degree-of-freedom system with a first-order time derivative term. Following the procedure of the Lefschetz thimble method, we explicitly evaluate the path integral for the generating function of the Noether charge and derive its exact transseries expression. Using the conservation law, we find all the complex saddle points of the action, which are responsible for the non-perturbative effects and the resurgence structure of the model. The all-order power-series contributions around each saddle point are generated from the one-loop determinant with the help of the differential equations obeyed by the generating function. The transseries are constructed by summing up the contributions from all the relevant saddle points, which we identify by determining the intersection numbers between the dual thimbles and the original path integration contour. We confirm that the Borel ambiguities of the perturbation series are canceled by the non-perturbative ambiguities originating from the discontinuous jumps of the intersection numbers. The transseries computed in the path-integral formalism agrees with the exact generating function, whose explicit form can be obtained in the operator formalism thanks to the integrable nature of the model. This agreement indicates the non-perturbative completeness of the transseries obtained by the semi-classical expansion of the path integral based on the Lefschetz thimble method.

hep-th↗
arXiv2021

Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models

The resurgence structure of the 2d $O(N)$ sigma model at large $N$ is studied with a focus on an IR momentum cutoff scale $a$ that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and correlators are derived as series of the dynamical scale $Λ$ (nonperturbative exponential) and coupling $λ_μ$ renormalized at the momentum scale $μ$. While there is no ambiguity when $a > Λ$, we find for $a < Λ$ that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector. These ambiguities arise as a result of an analytic continuation of transseries coefficients to small values of the IR cutoff $a$ below the dynamical scale $Λ$. We find that the imaginary ambiguities are cancelled each other when we take all of them into account. By comparing the semiclassical expansion with the transseries for the exact large-$N$ result, we find that some ambiguities vanish in the $a \rightarrow 0$ limit and hence the resurgence structure changes when going from the semiclassical expansion to the exact result with no IR cutoff. An application of our approach to the ${\mathbb C}P^{N-1}$ sigma model is also discussed. We find in the compactified model with the ${\mathbb Z}_N$ twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied.

hep-th↗
arXiv2021

Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED

We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from the SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.

hep-th↗
arXiv2021

Exact WKB analysis of the vacuum pair production by time-dependent electric fields

We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis. We identify the generic structure of a Stokes graph for systems with the vacuum pair production and show that the number of produced pairs is given by a product of connection matrices for Stokes segments connecting pairs of turning points. We derive an explicit formula for the number of produced pairs, assuming the semi-classical limit. The obtained formula can be understood as a generalization of the divergent asymptotic series method by Berry, and is consistent with other semi-classical methods such as the worldline instanton method and the steepest descent evaluation of the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula to discuss effects of time-dependence of the applied strong electric field including the interplay between the perturbative multi-photon pair production and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger mechanism.

hep-th↗
arXiv2020

Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism

We develop the effective field theoretical descriptions of spin systems in the presence of symmetry-breaking effects: the magnetic field, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice description of spin systems, we show that the symmetry-breaking terms corresponding to the above effects can be incorporated into the effective field theory as a combination of a background (or spurious) $\SO(3)$ gauge field and a scalar field in the symmetric tensor representation, which are eventually fixed at their physical values. We use the effective field theory to investigate mode spectra of inhomogeneous ground states, with focusing on one-dimensionally inhomogeneous states, such as helical and spiral states. Although the helical and spiral ground states share a common feature of supporting the gapless Nambu-Goldstone modes associated with the translational symmetry breaking, they have qualitatively different dispersion relations: isotropic in the helical phase while anisotropic in the spiral phase. We also discuss the magnon production induced by an inhomogeneous magnetic field, and find a formula akin to the Schwinger formula. Our formula for the magnon production gives a finite rate for antiferromagnets, and a vanishing rate for ferromagnets, whereas that for ferrimagnets interpolates between the two cases.

cond-mat.mes-hall↗
arXiv2020

Lattice ${\mathbb C} P^{N-1}$ model with ${\mathbb Z}_{N}$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy

We investigate the lattice ${\mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $\times$ $S_τ^{1}$(small) with the ${\mathbb Z}_{N}$ symmetric twisted boundary condition, where a sufficiently large ratio of the circumferences ($L_{s}\gg L_τ$) is taken to approximate ${\mathbb R} \times S^1$. We find that the expectation value of the Polyakov loop, which is an order parameter of the ${\mathbb Z}_N$ symmetry, remains consistent with zero ($|\langle P\rangle|\sim 0$) from small to relatively large inverse coupling $β$ (from large to small $L_τ$). As $β$ increases, the distribution of the Polyakov loop on the complex plane, which concentrates around the origin for small $β$, isotropically spreads and forms a regular $N$-sided-polygon shape (e.g. pentagon for $N=5$), leading to $|\langle P\rangle| \sim 0$. By investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, we also verify the existence of fractional instantons and bions, which cause tunneling transition between the classical $N$ vacua and stabilize the ${\mathbb Z}_{N}$ symmetry. Even for quite high $β$, we find that a regular-polygon shape of the Polyakov-loop distribution, even if it is broken, tends to be restored and $|\langle P\rangle|$ gets smaller as the number of samples increases. To discuss the adiabatic continuity of the vacuum structure from another viewpoint, we calculate the $β$ dependence of ``pseudo-entropy" density $\propto\langle T_{xx}-T_{ττ}\rangle$. The result is consistent with the absence of a phase transition between large and small $β$ regions.

hep-th↗
arXiv2019

Lattice study on the twisted ${\mathbb C}P^{N-1}$ models on ${\mathbb R}\times S^{1}$

We report the results of the lattice simulation of the ${\mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $\times$ $S_τ^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${\mathbb R} \times S^1$. For periodic boundary condition imposed in the $S_τ^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${\mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $β$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${\mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${\mathbb Z}_{N}$ vacua.

hep-lat↗
arXiv2019

Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}P^{N-1}$ Model

The $\mathbb{C}P^{N-1}$ sigma model at finite temperature is studied using lattice Monte Carlo simulations on $S_{s}^{1} \times S_τ^{1}$ with radii $L_{s}$ and $L_τ$, respectively, where the ratio of the circumferences is taken to be sufficiently large ($L_{s}/L_τ \gg 1$) to simulate the model on $\mathbb{R} \times S^1$. We show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as $L_τ$ is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. We find that the global PSU($N$)=SU($N$)$/{\mathbb Z}_{N}$ symmetry remains unbroken at "quantum" and "classical" levels for the small and large $L_τ$, respectively: in the small $L_τ$ region for finite $N$, the order parameter fluctuates extensively with its expectation value consistent with zero after taking an ensemble average, while in the large $L_τ$ region the order parameter remains small with little fluctuations. We also calculate the thermal entropy and find that the degrees of freedom in the small $L_τ$ regime are consistent with $N-1$ free complex scalar fields, thereby indicating a good agreement with the prediction from the large-$N$ study for small $L_τ$.

hep-th↗
arXiv2019

Instantons in Chiral Magnets

We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the $O(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.

cond-mat.mes-hall↗
arXiv2018

Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories

We study a certain class of supersymmetric (SUSY) observables in 3d $\mathcal{N}=2$ SUSY Chern-Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have nontrivial resurgent structures by expressing the exact results as a full transseries consisting of perturbative and non-perturbative parts. As real mass parameters are varied, we encounter Stokes phenomena at an infinite number of points, where the perturbative series becomes non-Borel-summable due to singularities on the positive real axis of the Borel plane. We also investigate the Stokes phenomena when the phase of the coupling constant is varied. For these cases, we find that the Borel ambiguities in the perturbative sector are canceled by those in nonperturbative sectors and end up with an unambiguous result which agrees with the exact result even on the Stokes lines. We also decompose the Coulomb branch localization formula, which is an integral representation for the exact results, into Lefschetz thimble contributions and study how they are related to the resurgent transseries. We interpret the non-perturbative effects appearing in the transseries as contributions of complexified SUSY solutions which formally satisfy the SUSY conditions but are not on the original path integral contour.

hep-th↗
arXiv2018

Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb C P^{N-1}$ models

We derive the semiclassical contributions from the real and complex bions in the two-dimensional $\mathbb C P^{N-1}$ sigma model on ${\mathbb R} \times S^{1}$ with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the $\mathbb C P^{N-1}$ quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find that the non-perturbative contribution vanishes in the supersymmetric case and it has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity in non-supersymmetric cases. This is the first explicit result indicating the relation between the complex bion and the infrared renormalon.

hep-th↗
arXiv2018

Domain Wall and Three Dimensional Duality

We discuss 1/2 BPS domain walls in the 3d $\mathcal N=4$ supersymmetric gauge theory which is self-dual under the 3d mirror symmetry. We find that if a BF-type coupling is introduced, invariance of the BPS domain wall under the duality transformation can be explicitly seen from the classical BPS equations. It has been known that particles and vortices are swapped under the 3d duality transformations. We show that Noether charges and vortex topological charges localized on the domain walls are correctly exchanged under the 3d mirror symmetry.

hep-th↗
arXiv2018

Ghostbusters in $f(R)$ supergravity

$f(R)$ supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains $R^n$ with $n$ greater than two.We remove the ghost in $f(R)$ supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism~\cite{Fujimori:2016udq}. We show that the mechanism removes the ghost supermultiplet but also terms including $R^n$ with $n\geq3$, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.

hep-th↗