arXiv subjects

Hidenori Fukaya

Publications and source records attributed to Hidenori Fukaya.

At least 55 records · Page 3Linked to original sources

arXiv2020

TKNN formula for general lattice Hamiltonian in odd dimensions

Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including non-minimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta.

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arXiv2020

TKNN formula for general Hamiltonian

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arXiv2020

Why is quantum gravity so difficult (compared to QCD)?

Gravity is difficult to quantize. This is a well-known fact but its reason is given simply by non-renormalizability of the Newton constant and little is discussed why among many quantum gauge theories, gravity is special. In this essay we try to treat the gravity as one of many gauge theories, and discuss how it is special and why it is difficult to quantize.

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arXiv2020

Axial U(1) symmetry and mesonic correlators at high temperature in $N_f=2$ lattice QCD

We investigate the high-temperature phase of QCD using lattice QCD simulations with $N_f = 2$ dynamical Möbius domain-wall fermions. On generated configurations, we study the axial $U(1)$ symmetry, overlap-Dirac spectra, screening masses from mesonic correlators, and topological susceptibility. We find that some of the observables are quite sensitive to lattice artifacts due to a small violation of the chiral symmetry. For those observables, we reweight the Möbius domain-wall fermion determinant by that of the overlap fermion. We also check the volume dependence of observables. Our data near the chiral limit indicates a strong suppression of the axial $U(1)$ anomaly at temperatures $\geq$ 220 MeV.

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arXiv2020

The Anomaly Inflow of the domain-wall fermion in odd dimension

In 1985, Callan and Harvey showed a view of gauge anomaly as a missing current into an extra-dimension, and the total contribution, including the Chern-Simons current in the bulk, is conserved. However in their computation, the edge and bulk contributions are separately evaluated and their cross correlations, which should be relevant at boundary, are simply ignored. This issue has been solved in many approaches. In this work, we revisit this issue with a complete set of eigenstates of free domain-wall Hamiltonian and give the systematic evaluation, easy to take in the higher mass correction and extend to the higher dimension.

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arXiv2020

A lattice formulation of the Atiyah-Patodi-Singer index

Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz et al. But its extension to the system with boundary (the so-called Atiyah- Patodi-Singer index theorem), which plays a crucial role in T-anomaly cancellation between bulk- and edge-modes in 3+1 dimensional topological matters, is known only in the continuum theory and no lattice realization has been made so far. In this work, we try to non-perturbatively define an alternative index from the lattice domain-wall fermion in 3+1 dimensions. We will show that this new index in the continuum limit, converges to the Atiyah-Patodi-Singer index defined on a manifold with boundary, which coincides with the surface of the domain-wall.

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arXiv2020

A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification

The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a non-local and unnatural boundary condition known as the "APS boundary condition" by hand. In 2017, we showed that the same integer as the APS index can be obtained from the $η$ invariant of the domain-wall Dirac operator. Recently we gave a mathematical proof that the equivalence is not a coincidence but generally true. In this contribution to the proceedings of LATTICE 2019, we try to explain the whole story in a physicist-friendly way.

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arXiv2019

Axial U(1) symmetry, topology, and Dirac spectra at high temperature in $N_f=2$ lattice QCD

Using lattice QCD simulations with $N_f = 2$ dynamical fermions, we study the axial $U(1)$ symmetry, topological charge, and Dirac eigenvalue spectra in the high-temperature phase in which the chiral symmetry is restored. Our gauge ensembles are generated with Möbius domain-wall fermions, but the measurements such as susceptibilities are reweighted to those for the overlap fermions by using overlap/domain-wall reweighting technique. We find that the $U(1)_A$ and topological susceptibilities are strongly suppressed in the small quark mass region, which is related to the reduction of chiral-zero and low-nonzero modes on the Dirac spectra. We also examine their volume dependence.

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arXiv2018

Axial U(1) symmetry and Dirac spectra in high-temperature phase of $N_f=2$ lattice QCD

The axial $U(1)$ symmetry in the high-temperature phase is investigated with $N_f = 2$ lattice QCD simulations. The gauge ensembles are generated with Möbius domain-wall fermions, and the overlap/domain-wall reweighting is applied. We find that the $U(1)_A$ susceptibility evaluated from the spectrum of overlap-Dirac eigenvalues is strongly suppressed in the chiral limit. We also study its volume dependence.

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arXiv2018

$B \to D^{(*)}\ellν$ form factors from $N_f\!=\!2+1$ QCD with Möbius domain-wall quarks

We report on our study of the B \to D^(*) \ell νsemileptonic decays at zero and nonzero recoils in 2+1 flavor QCD. The Möbius domain-wall action is employed for light, charm and bottom quarks at lattice cutoffs 1/a = 2.5 and 3.6 GeV. We take bottom quark masses up to \approx 2.4 times the physical charm mass to control discretization effects. The pion mass is as low as M_π\sim 310 MeV. We present our preliminary results for the relevant form factors and discuss the violation of heavy quark symmetry, which is a recent important isuue on the long-standing tension in the Cabibbo-Kobayashi-Maskawa matrix element |V_{cb}| between the exclusive and inclusive decays.

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arXiv2018

Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD

The eigenvalue spectrum $ρ(λ)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract them at the leading order and then take the continuum limit with lattice data at three lattice spacings. Lattice results for the exponent $\partial\lnρ/\partial\lnλ$ are matched to continuum perturbation theory, which is known up to $O(α_s^4)$, to extract the strong coupling constant $α_s$.

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arXiv2018

Can axial U(1) anomaly disappear at high temperature?

In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition. Our simulation data also indicate suppression of topological susceptibility. In this talk, we present both of our theoretical and numerical evidence for disappearance of axial U(1) anomaly, emphasizing the importance of controlling lattice chiral symmetry violation, which is enhanced at high temperature.

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arXiv2018

Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator

The Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical set-up for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a non-local boundary condition known as the "APS boundary condition" by hand, which is unlikely to be realized in the materials. In this work, we attempt to reformulate the APS index in a "physicist-friendly" way for a simple set-up with $U(1)$ or $SU(N)$ gauge group on a flat four-dimensional Euclidean space. We find that the same index as APS is obtained from the domain-wall fermion Dirac operator with a local boundary condition, which is naturally given by the kink structure in the mass term. As the boundary condition does not depend on the gauge fields, our new definition of the index is easy to compute with the standard Fujikawa method.

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arXiv2017

Topological susceptibility in 2+1-flavor QCD with chiral fermions

We compute the topological susceptibility $χ_t$ of 2+1-flavor lattice QCD with dynamical Möbius domain-wall fermions, whose residual mass is kept at 1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a "slab" sub-volume of the simulated lattice, as proposed by Bietenholz et al. The quark mass dependence of our results agrees well with the prediction of the chiral perturbation theory, from which the chiral condensate is extracted. Combining the results for the pion mass $M_π$ and decay constant $F_π$, we obtain $χ_t$ = 0.227(02)(11)$M_π^2 F_π^2$ at the physical point, where the first error is statistical and the second is systematic.

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arXiv2017

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

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arXiv2017

D meson semileptonic form factors in Nf=3 QCD with Möbius domain-wall quarks

We present our calculation of D \to pi and D \to K semileptonic form factors in Nf = 2+1 lattice QCD. We simulate three lattice cutoffs 1/a \sim 2.5, 3.6 and 4.5 GeV with pion masses as low as 230 MeV. The Möbius domain-wall action is employed for both light and charm quarks. We present our results for the vector and scalar form factors and discuss their dependence on the lattice spacing, light quark masses and momentum transfer.

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arXiv2017

Axial $U(1)$ symmetry at high temperature in 2-flavor lattice QCD

We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical Möbius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 \, \mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.

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arXiv2017

Dirac spectral density and mass anomalous dimension in 2+1 flavor QCD

We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings ($a=0.083, 0.055, 0.044$ fm) to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to $O(α_s^4)$.

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