Hidenori Fukaya

Low-Lying Mode Contribution to the Quenched Meson Correlators in the ε-Regime

We present a quenched calculation of meson correlators using the overlap fermion with very small masses, 2.6-13 MeV. In this region, the pion Compton wavelength is larger than our lattice size (L ≃ 1.23 fm), and the system is in the so-called e-regime of chiral perturbation theory. We find that the scalar and pseudo-scalar correlators are accurately approximated by a few hundred low-lying fermion eigenmodes in this regime, whereas the axial-vector correlator contains significant contributions from higher eigenmodes. We also compute the disconnected pseudo-scalar correlator, which is well saturated with low-lying modes. Matching these lattice data with the one-loop expressions for the correlators in quenched chiral perturbation theory, we evaluate the decay constant F π and the chiral condensate Σ, as well as the parameters m 2 0 and α, which describe the artifacts of the quenched approximation.

Lattice study of the massive Schwinger model with a φ term under Lüscher's “Admissibility” condition☆

Abstract We present a numerical study of the massive two-flavor QED in two dimensions with the gauge action proposed by Luscher, which allows only “admissible” gauge fields. We find that the admissibility condition does not allow any topology changes by the local updation in Hybrid Monte Carlo algorithm so that the configurations in each topological sector can be generated separately. By developing a new method to sum over different topological sectors, we investigate θ vacuum effects. Combining with domain-wall fermion action, we obtain the fermion mass dependence and θ dependence of the meson masses, which are consistent with the analytic results by mass perturbation in the continuum theory.

Note on Massless Bosonic States in Two-Dimensional Field Theories

In this paper, we show that in a wide class of GL ×GR invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents can be determined to all orders in perturbation theory. The twopoint function possesses a massless pole for any non-trivial fermion content, and this fact provides a simple criterion to determine the existence of massless bosonic physical states without solving the dynamics. Our argument is based on anomalous Ward-Takahashi (WT) identities and is somewhat similar to that for the ’t Hooft anomaly matching condition. 1)–3) In fact, applying the anomaly matching argument to the systems we consider (assuming that the anomalous behavior of the two-point function does not receive higher-order radiative corrections), one would arrive at a similar conclusion concerning massless states. (See, for example, Refs. 4)–6).) The point of this paper is, however, to show that in the two-dimensional systems we consider, an elementary argument suffices to obtain an explicit form of the twopoint function to all orders in perturbation theory. In particular, our argument is applicable even to systems in which the left and right moving modes are not

Overlap/Domain-wall reweighting

We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the eigenvalues are not significantly affected. We discuss the possibility of reweighting the gauge configurations generated with domain-wall fermions to those of exactly chiral lattice fermions.

Overlap fermion with the topology conserving gauge action

We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator,

Topological Susceptibility in Nf = 2 QCD at Finite Temperature

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

, with the gauge action whose form is designed to avoid topology change, as well as with the standard plaquette action. On the quenched lattices, the former gauge action exhibits less density of low-lying eigenmodes of

Topological quantum fluctuations in lattice QCD with overlap Dirac quarks

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Theta vacuum effects on the pseudoscalar condensates and the η′ meson in 2-dimensional lattice QED☆

compared to the latter at the same lattice spacing. We also show preliminary results for the dynamical simulation with two flavors of overlap fermions.

Fine lattice simulations with chirally symmetric fermions

We study the topological charge in Nf = 2 QCD at finite temperature using Mobius domain-wall fermions. The susceptibility Xt of the topological charge defined either by the index of overlap Dirac operator or a gluonic operator is investigated at several values of temperature T (> Tc ) varying the quark mass. A strong suppression of the susceptibility is observed below a certain value of the quark mass. The relation with the restoration of UA (1) is discussed.