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Yoshio Kikukawa

Publications and source records attributed to Yoshio Kikukawa.

At least 19 recordsLinked to original sources
arXiv2026

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation

We study the duality structure of lattice Maxwell theory with a theta term in the Hamiltonian Villain formulation. Reflecting the fact that odd-level Chern--Simons theory depends on a choice of spin structure, a complete realization of the full $\mathrm{SL}(2,\mathbb{Z})$ structure would require fermionic degrees of freedom. We therefore restrict our analysis to the bosonic theory and focus on the theta subgroup generated by the $\mathcal{S}$ and $\mathcal{T}^{2}$ transformations. We construct these transformations at the operator level and show that they realize the theta subgroup structure of $\mathrm{SL}(2,\mathbb Z)$. We also extend the analysis to sectors with electric and magnetic charges, introduced as violations of the Gauss-law constraint and the Bianchi identity, respectively. We show that the $\mathcal S$ transformation exchanges electric and magnetic charges, while the $\mathcal T^2$ transformation realizes the Witten effect. Finally, we discuss a related non-invertible defect obtained by gauging a $\mathbb Z_N$ subgroup of the global $\mathrm{U}(1)$ $1$-form symmetry, and show that its fusion rule reproduces the expected Tambara--Yamagami structure.

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arXiv2026

Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $θ$-term in Modified Villain Formulation

We study the duality of lattice Maxwell theory in the modified Villain formulation, employing an ultra-local action with a theta term. Although this action is known to become non ultra-local through the Poisson resummation formula, we show that this non ultra-locality can be removed by incorporating a non-local transformation procedure into the definition of the S-transformation. As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops. This effect originates from the non-local transformation procedure in the S-transformation. Remarkably, the resulting SL(2,Z)-structure closely resembles that of non-spin Maxwell theory.

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arXiv2026

Chiral Anomaly of Kogut-Susskind Fermion in the (3+1)-dimensional Hamiltonian formalism

We consider Kogut-Susskind fermions (also known as staggered fermions) in a $(3+1)$-dimensional Hamiltonian formalism and examine a chiral transformation and its associated chiral anomaly. The Hamiltonian of the massless Kogut-Susskind fermion has symmetry under the shift transformations in each space direction $S_k \, (k=1,2,3)$, and the product of the three shift transformations in particular (the odd shifts in general) may be regarded as a unitary discrete chiral transformation, modulo two-site translations. The hermitian part of the transformation kernel $Γ= i S_1 S_2 S_3$ can define an axial charge as $Q_A = (1/2)\sum_x χ^\dagger(x) \left(Γ+Γ^\dagger \right)χ(x)$, which is non-onsite, nonquantized, and commutative with the vector charge, analogous to $\tilde{Q}_A = (1/2) \sum_n ( χ^\dagger_n χ_{n+1} + χ^\dagger_{n+1} χ_{n} )$ for the $(1+1)$ dimensional Kogut-Susskind fermion. However, our $Q_A$ cannot be expressed in terms of any quantized charges in a generalized Onsager algebra. Although $Q_A$ does not commute with the fermion Hamiltonian in general when coupled to background link gauge fields, we show that they become commutative for a class of $U(1)$ link configurations carrying nontrivial magnetic and electric fields. We then verify numerically that the vacuum expectation value of $Q_A$ satisfies the anomalous conservation law of axial charge in the continuum two-flavor theory under an adiabatic evolution of the link gauge field.

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arXiv2025

Critical behavior of the Schwinger model via gauge-invariant VUMPS

We study the lattice Schwinger model by combining the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with $θ=π$ are known to exhibit first-order phase transitions for the values of the fermion mass above a critical value, where a second-order phase transition occurs. Our algorithm enables a precise determination of the critical endpoint in the continuum theory. We further analyze the scaling in the simultaneous critical and continuum limits and confirm that the data collapse aligns with the Ising universality class to remarkable precision.

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arXiv2020

On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories

We examine the proposal by Grabowska and Kaplan (GK) to use the infinite gradient flow in the domain-wall formulation of chiral lattice gauge theories. We consider the case of Abelian theories in detail, for which Lüscher's exact gauge-invariant formulation is known, and we relate GK's formulation to Lüscher's one. The gradient flow can be formulated for the admissible U(1) link fields so that it preserves their topological charges. GK's effective action turns out to be equal to the sum of Lüscher's gauge-invariant effective actions for the target Weyl fermions and the mirror "fluffy" fermions, plus the so-called measureterm integrated along the infinite gradient flow. The measure-term current is originally a local(analytic) and gauge-invariant functional of the admissible link field, given as a solution to the local cohomology problem. However, with the infinite gradient flow, it gives rise to non-local(non-analytic) vertex functions which are not suppressed exponentially at large distance. The "fluffy" fermions remain as a source of non-local contribution, which couple yet to the Wilson-line and magnetic-flux degrees of freedom of the dynamical link field.

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arXiv2018

On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)

We consider the lattice formulation of SO(10) chiral gauge theory with left-handed Weyl fermions in the sixteen dimensional spinor representation ($\underline{16}$) within the framework of the Overlap fermion/the Ginsparg-Wilson relation. We define a manifestly gauge-invariant path-integral measure for the left-handed Weyl field using all the components of the Dirac field, but the right-handed part of which is just saturated completely by inserting a suitable product of the SO(10)-invariant 't Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the 't Hooft vertices. There remains the issue of locality in the gauge-field dependence of the Weyl fermion measure, but the question can be addressed in the weak gauge-coupling expansion at least using Monte Carlo methods without encountering the sign problem. We also discuss the relations of our formulation to other approaches/proposals to decouple the species-doubling/mirror degrees of freedom. Those include Eichten-Preskill model, Ginsparg-Wilson Mirror-fermion model, Domain wall fermion model with the boundary Eichten-Preskill term, 4D Topological Insulator/Superconductor with gapped boundary phase, and the recent studies on the PMS phase/"Mass without symmetry breaking". We clarify the similarity and the difference in technical detail and show that our proposal is a well-defined testing ground for that basic question.

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arXiv2018

Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories

In the mirror fermion approach with Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 345 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two-point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the PMS phase. We re-examine why the attempt seems a "Mission: Impossible" in the 345 model. We point out that the effective operators to break the fermion number symmetries ('t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We observe also that the type of Majorana mass term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature. We then consider a simpler four-flavor axial gauge model, the 1$^4$(-1)$^4$ model, in which the U(1)$_A$ gauge and Spin(6)(SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. In the strong-coupling limit of the quartic operators, the model is well-behaved and simplified. Through Monte-Carlo simulations in the weak gauge coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior, and we still argue that all you need is killing the continuous mirror-fermion symmetries with would-be gauge anomalies non-matched. Finally, by gauging a U(1) subgroup of the U(1)$_A$$\times$ Spin(6)(SU(4)) of the previous model, we formulate the $2 1 (-1)^3$ chiral gauge model and argue that the induced fermion measure term satisfies the required locality property and provides a solution to the reconstruction theorem.

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arXiv2017

Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density

Statistical sampling with the complex Langevin (CL) equation is applied to (0+1)-dimensional Thirring model, and its uniform-field variant, at finite fermion chemical potential $μ$. The CL simulation reproduces a crossover behavior which is similar to but actually deviating from the exact solution in the transition region, where we confirm that the CL simulation becomes susceptible to the drift singularities, i.e., zeros of the fermion determinant. In order to simulate the transition region with the CL method correctly, we examine two approaches, a reweighting method and a model deformation, in both of which a single thimble with an attractive fixed point practically covers the integration domain and the CL sampling avoids the determinant zeros. It turns out that these methods can reproduce the correct crossover behavior of the original model with using reference ensembles in the complexified space. However, they need evaluation of the reweighting factor, which scales with the system size exponentially. We discuss feasibility of applying these methods to the Thirring model and to more realistic theories.

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arXiv2016

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling $β$ and/or large lattice size $L$, while they are in good agreement at the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit keeping the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model's thimble structure. And these results imply that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.

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arXiv2015

Application of the Lefschetz thimble formulation to the (0+1) dim. Thirring model at finite density

Based on the Lefschetz thimble formulation of path-integration, we analyze the (0+1) dimensional Thirring model at finite chemical potentials and perform hybrid Monte Carlo (HMC) simulations. We adopt the lattice action defined with the staggered fermion and a compact link field for the auxiliary vector field. We firstly locate the critical points (saddle points) of the gradient flows within the subspace of time-independent (complex) link field, and study the thiemble structure and the Stokes phenomenon to identify the thimbles which contribute to the path-integral. Then, we perform HMC simulations on the single dominant thimble and compare the results to the exact solution. The numerical results are in agreement with the exact ones in small and large chemical potential regions, while they show some deviation in the crossover region in the chemical potential. We also comment on the necessity of the contributions from multiple thimbles in the crossover region.

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arXiv2014

Lattice simulation of SU(2) gauge theory with chirally symmetric fermions

We numerically study the SU(2) gauge theory with two dynamical flavors of the domain-wall fermions in fundamental representation. The meson spectra and the residual mass are measured on three lattice volumes and at two values of gauge coupling so as to investigate the finite volume effect. On generated configurations, eigenvalues of the overlap fermion operator are determined and compared to the random matrix theory. To quantify the effect of violation of the exact chiral symmetry, we measure the correlation between the eigenvectors of the domain-wall and the overlap operators.

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arXiv2012

Reflection Positivity of N=1 Wess-Zumino model on the lattice with exact U(1)_R symmetry

By using overlap Majorana fermions, the ${\cal N}=1$ chiral multiple can be formulated so that the supersymmetry is manifest and the vacuum energy is cancelled in the free limit, thanks to the bilinear nature of the free action. It is pointed out, however, that in this formulation the reflection positivity is violated in the bosonic part of the action, although it is satisfied in the fermionic part. It is found that the positivity of the spectral density of the bosonic two-point correlation function is ensured only for the spacial momenta $a | p_k | \lesssim 1.72$ $(k=1,2,3)$. It is then argued that in formulating ${\cal N}=1$ Wess-Zumino model with the overlap Majorana fermion, one may adopt a simpler nearest-neighbor bosonic action, discarding the free limit manifest supersymmetry. The model still preserves the would-be U(1)$_R$ symmetry and satisfies the reflection positivity.

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arXiv2010

Reflection Positivity of Free Overlap Fermions

It is shown that free lattice fermions defined by overlap Dirac operator fulfill the Osterwalder-Schrader reflection positivity condition with respect to the link-reflection. The proof holds true in non-gauge models with interactions such as chiral Yukawa models.

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arXiv2010

A lattice study of N=2 Landau-Ginzburg model using a Nicolai map

It has been conjectured that the two-dimensional N=2 Wess-Zumino model with a quasi-homogeneous superpotential provides the Landau-Ginzburg description of the N=2 superconformal minimal models. For the cubic superpotential W=(lambda) Phi^3/3, it is expected that the Wess-Zumino model describes A_{2} model and the chiral superfield Phi shows the conformal weight (h,bar{h})=(1/6,1/6) at the IR fixed point. We study this conjecture by a lattice simulation, extracting the weight from the finite volume scaling of the susceptibility of the scalar component in Phi. We adopt a lattice model with the overlap fermion, which possesses a Nicolai map and a discrete R-symmetry. We set a(lambda)=0.3 and generate the scalar field configurations by solving the Nicolai map on L times L lattices in the range L=18 - 32. To solve the map, we use the Newton-Raphson algorithm with various initial configurations. The result is 1-h-bar{h}=0.660 \pm0.011, which is consistent with the conjecture within the statistical error, while a systematic error is estimated as less than 0.5 %.

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arXiv2008

Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry

In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N=(2,2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattice formulation of matter multiplets charged only under the central U(1) (the overall U(1)) of the gauge group G=U(N), and then construct lattice models for gauged linear sigma models with exactly preserving one supercharge and their chiral flavor symmetry.

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arXiv2008

A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.

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arXiv2008

A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in a finite volume. The resulted formula is very close to the known expression of the measure term in the infinite volume with a single parameter integration, and would be useful in practical implementations.

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