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Categorification of invariants in gauge theory and sypmplectic geometryMar 02 2017This is a mixture of survey article and research anouncement. We discuss Instanton Floer homology for 3 manifolds with boundary. We also discuss a categorification of the Lagrangian Floer theory using the unobstructed immersed Lagrangian correspondence ... More

S-parameter and pseudo-Nambu-Goldstone boson mass from lattice QCDJun 26 2008Dec 03 2008We present a lattice calculation of $L_{10}$, one of the low energy constants in Chiral Perturbation Theory, and the charged-neutral pion squared mass splitting, using dynamical overlap fermion. Exact chiral symmetry of the overlap fermion allows us to ... More

Partially quenched chiral perturbation theory in the epsilon-regimeJul 25 2007Aug 21 2007We calculate meson correlators in the epsilon-regime within partially quenched chiral perturbation theory. The valence quark masses and sea quark masses can be chosen arbitrary and all non-degenerate. Taking some of the sea quark masses to infinity, one ... More

The Chiral Condensate in a Finite VolumeDec 15 2008Sep 18 2009Chiral perturbation theory at finite four-volume V (=L^3T) is reconsidered with a view towards finding a computational scheme that can deal with any value of M_\pi L, where M_\pi is a generic Nambu-Goldstone mass. The momentum zero modes that cause the ... More

Symmetries of spatial meson correlators in high temperature QCDFeb 08 2019Based on a complete set of $J = 0$ and $J=1$ spatial isovector correlation functions calculated with $N_F = 2$ domain wall fermions we identify an intermediate temperature regime of $T \sim 250 - 550$ MeV where chiral symmetry is restored but the correlators ... More

A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjectureMay 16 2017Jan 16 2018We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy the coarse ... More

Finite-volume Correction to the Pion Decay Constant in the Epsilon-RegimeNov 01 2007Aug 07 2008In the chiral limit of QCD, the pion decay constant F can be extracted from lattice gauge theory by means of a coupling to isospin chemical potential. Here we compute the leading correction due to finite volume in the epsilon-expansion of chiral perturbation ... More

Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCDAug 14 2008Oct 18 2008We consider chiral perturbation theory in a finite volume and in a mixed regime of quark masses. We take N_l light quarks near the chiral limit, in the so-called epsilon-regime, while the remaining N_h quarks are heavier and in the standard p-regime. ... More

Canonical models of filtered $A_\infty$-algebras and Morse complexesDec 10 2008The purpose of this paper is two-fold. First we explain the construction of the canonical model of filtered $A_\infty$-algebras given in the authors' book [FOOO]. The canonical model plays a crucial role in the study of Lagrangian Floer theory on toric ... More

Parameter dependence of the topology change and the scaling properties of the topology conserving gauge actionSep 30 2005Nov 10 2005The topology conserving gauge action proposed by Luescher is expected to reduce the number of non-smooth gauge configurations as well as the topology change compared to the conventional actions for the same lattice spacings. We report our quenched QCD ... More

Stochastic calculation of the QCD Dirac operator spectrum with Mobius domain-wall fermionJan 05 2016We calculate the spectral function of the QCD Dirac operator using the four-dimensional effective operator constructed from the Mobius domain-wall implementation. We utilize the eigenvalue filtering technique combined with the stochastic estimate of the ... More

Lagrangian Floer theory on compact toric manifolds IFeb 12 2008Sep 05 2009The present authors introduced the notion of \emph{weakly unobstructed} Lagrangian submanifolds and constructed their \emph{potential function} $\mathfrak{PO}$ purely in terms of $A$-model data in [FOOO2]. In this paper, we carry out explicit calculations ... More

Topology conserving gauge action and the overlap-Dirac operatorOct 28 2005Dec 09 2005We apply the topology conserving gauge action proposed by Luescher to the four-dimensional lattice QCD simulation in the quenched approximation. With this gauge action the topological charge is stabilized along the hybrid Monte Carlo updates compared ... More

Extracting the $η^\prime$ meson mass from gluonic correlators in lattice QCDNov 12 2015Calculation of the eta-prime meson mass is a notoriously difficult problem, as it requires evaluation of the disconnected diagram which is costly and noisy. In this work, we use a gluonic operator to extract the eta-prime state after smearing the link ... More

Counting pseudo-holomorphic discs in Calabi-Yau 3 foldAug 02 2009n this paper we define an invariant of a pair of 6 dimensional symplectic %optional manifold with vanishing 1st Chern class and its Lagrangian submanifold with vanishing Maslov index. This invariant is a function on the set of the path connected components ... More

The chiral limit in lattice QCDFeb 26 2007Mar 11 2007It has been a big challenge for lattice QCD to simulate dynamical quarks near the chiral limit. Theoretically, it is well-known that the naive chiral symmetry cannot be realized on the lattice (the Nielsen-Ninomiya theorem). Also practically, the computational ... More

Sublinear Higson corornae of Euclidean conesFeb 25 2010The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric ... More

Coarse dynamics and fixed point propertyDec 18 2008We investigate the fixed point property of the group actions on a coarse space and its Higson corona. We deduce the coarse version of Brouwer's fixed point theorem.

Application of Groebner bases to the cup-length of oriented Grassmann manifoldsOct 22 2007Jan 15 2008We determine the cup-length of some oriented Grassmann manifolds by finding a Groebner basis associated with a certain subring of the cohomology of them. As its applications, we provide not only a lower but also an upper bound for the LS-category of some ... More

Cyclic symmetry and adic convergence in LagrangianFloer theoryJul 24 2009In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve, in the case of real coefficient, the construction of Lagrangian Floer cohomology of which the author developed jointly with Oh-Ohta-Ono. ... More

Note on massless bosonic states in two-dimensional field theoriesSep 07 2006Dec 18 2006In a wide class of $G_L\times G_R$ invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents is completely determined by a fermion one-loop diagram. For any non-trivial fermion content, ... More

Floer homology of Lagrangian submanifoldsJun 24 2011This is a translation of an article appeared in Japanese in Suugaku 63 (2011), no. 1, 43-66 (MR2790665) and is a survey of Lagrangian Floer homology which the author studies jointly with Y.-G.Oh, H. Ohta, and K. Ono. It also contains some explanation ... More

Lattice QCD with fixed topologyMar 06 2006Jun 26 2006The overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, realizes exact chiral symmetry on the lattice without any unphysical doubler modes. To perform the path integrals, one should, however, note that the overlap fermion determinant ... More

Projective resolution of modules over the noncommutative algebraJun 08 2009We give an explicit algorithm to compute a projective resolution of a module over the noncommutative ring based on the noncommutative Groebner bases theory.

$SO(3)$-Floer homology of 3-manifolds with boundary 1Jun 03 2015In this paper the author discuss the relation between Lagrangian Floer homology and Gauge-theory (Donaldson theory) Floer homology. It can be regarded as a version of Atiyah-Floer type conjecture in the case of $SO(3)$-bundle with non-trivial second Stiefel-Whitney ... More

Lagrangian Floer theory on compact toric manifolds II : Bulk deformationsOct 31 2008Mar 05 2011This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian ... More

Overlap fermion with the topology conserving gauge actionOct 23 2005We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator, $H_W$, 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 ... More

Pion form factor from all-to-all propagators of overlap quarksOct 12 2007We report on our calculation of the pion electromagnetic form factor with two-flavors of dynamical overlap quarks. Gauge configurations are generated using the Iwasaki gauge action on a 16^3 \times 32 lattice at the lattice spacing of 0.12fm with sea ... More

Computation of the electromagnetic pion form factor from lattice QCD in the epsilon regimeMay 16 2014Sep 01 2014We calculate the electromagnetic pion form factor in lattice QCD with 2+1 flavors of the dynamical overlap quarks. Up and down quark masses are set below their physical values so that the system is in the so-called epsilon regime with the small size of ... More

Calculation of the nucleon sigma term and strange quark content with two flavors of dynamical overlap fermionsOct 23 2008We present a calculation of the nucleon sigma term on two-flavor QCD configurations with dynamical overlap fermions. We analyse the lattice data for the nucleon mass using the baryon chiral perturbation theory. Using partially quenched data sets, we extract ... More

Lattice study of 4d {\cal N}=1 super Yang-Mills theory with dynamical overlap gluinoNov 09 2011We report on a lattice simulation result for four-dimensional {\cal N}=1 SU(2) super Yang-Mills theory with the dynamical overlap gluino. We study the spectrum of the overlap Dirac operator at three different gluino masses m=0.2, 0.1 and 0.05 with the ... More

Pion mass difference from vacuum polarizationOct 03 2007We calculate the electromagnetic contribution to the pion mass difference, $\Delta m^2_\pi=m^2_{\pi^+}-m^2_{\pi^0}$, in the chiral limit through the $VV-AA$ type vacuum polarization using Das-Guralnik-Mathur-Low-Young (DGMLY) sum rule. The calculation ... More

Renormalization of domain-wall bilinear operators with short-distance current correlatorsApr 29 2016We determine the renormalization constants for flavor non-singlet fermion bilinear operators of M\"obius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the non-perturbative ... More

Topology density correlator on dynamical domain-wall ensembles with nearly frozen topological chargeNov 06 2014Nov 13 2014Global topological charge decorrelates very slowly or even freezes in fine lattice simulations. On the other hand, its local fluctuations are expected to survive and lead to the correct physical results as long as the volume is large enough. We investigate ... More

Large-scale simulations with chiral symmetryNov 27 2013We carry out a comparative study among five-dimensional formulations of chirally symmetric fermions about the algorithmic performance, chiral symmetry violation and topological tunneling to find a computationally inexpensive formulation with good chiral ... More

Analysis of short-distance current correlators using OPENov 30 2015We investigate the correlators of flavor non-singlet bilinear operators calculated on the lattice at short distances. In the continuum theory, non-perturbative effects are encoded in the form of the operator product expansion (OPE). We test the prediction ... More

Overlap/Domain-wall reweightingNov 19 2013We 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 ... More

Evidence of effective axial U(1) symmetry restoration at high temperature QCDDec 06 2016We study the axial U(1) symmetry at finite temperature in two-flavor lattice QCD. Employing the Mobius domain-wall fermions, we generate gauge configurations slightly above the critical temperature Tc with different lattice sizes L = 2-4 fm. Our action ... More

Light meson form factors in N_f=2+1 QCD with dynamical overlap quarksDec 01 2010We report on our calculation of pion and kaon form factors in three-flavor QCD using the overlap quark action. Gauge ensembles are generated on a 16^3 \times 48 lattice at a lattice spacing of 0.11 fm with pion masses down to 310 MeV. Connected and disconnected ... More

Strong coupling constant from vacuum polarization functions in three-flavor lattice QCD with dynamical overlap fermionsFeb 02 2010Sep 04 2014We determine the strong coupling constant $\alpha_s$ from a lattice calculation of vacuum polarization functions (VPF) in three-flavor QCD with dynamical overlap fermions. Fitting lattice data of VPF to the continuum perturbative formula including the ... More

$η^\prime$ meson mass from topological charge density correlator in QCDSep 03 2015Nov 20 2015The flavor-singlet component of the eta prime meson is related to the topological structure of the SU(3) gauge field through the chiral anomaly. We perform a 2+1-flavor lattice QCD calculation and demonstrate that the two-point function of a gluonically ... More

Nucleon sigma term and strange quark content in 2+1-flavor QCD with dynamical overlap fermionsOct 17 2009We study the sigma term and the strange quark content of nucleon in 2+1-flavor QCD with dynamical overlap fermions. We analyze the lattice data of nucleon mass taken at two different strange quark masses with five values of up and down quark masses each. ... More

Pion form factors in the epsilon regimeNov 05 2012We consider how to extract the pion form factors in the epsilon regime. Using the correlators with non-zero momenta and taking appropriate ratios of them, we eliminate the dominant finite volume effect from the zero-momentum pion mode. Our preliminary ... More

Meson correlators in the epsilon-regime of two-flavor lattice QCDOct 18 2007Nov 30 2007We calculate the meson correlators in the $\epsilon$-regime of two-flavor QCD. On a $16^3\times 32$ lattice with $a\sim 0.11$ fm, the lattice simulations are performed with the dynamical overlap fermions. We reduce the sea quark mass down to $\sim$ 3 ... More

Non-perturbative renormalization of bilinear operators with dynamical overlap fermionsJul 16 2009Using the non-perturbative renormalization technique, we calculate the renormalization factors for quark bilinear operators made of overlap fermions on the lattice. The background gauge field is generated by the JLQCD and TWQCD collaborations including ... More

Chiral interpolation in a finite volumeNov 02 2011A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of \sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior in a finite ... More

Dynamical overlap fermion at fixed topologyOct 02 2006We launched a project to perform dymanical fermion simulations using the overlap fermion formulation for sea quarks. In order to avoid the appearace of near-zero modes of the hermitian Wilson-Dirac operator $H_W$, we introduce a pair of extra Wilson fermions ... More

Light meson spectrum with $N_f=2$ dynamical overlap fermionsOct 04 2007We present numerical simulation of QCD with two dynamical quark flavors described by the overlap fermion action on a $16^3\times 32\times (0.12 {\rm fm})^4$ lattice. We calculate pseudo-scalar masses and decay constants and investigate their chiral properties. ... More

B_K with two flavors of dynamical overlap fermionsJan 28 2008May 11 2008We present a two-flavor QCD calculation of $B_K$ on a $16^3 \times 32$ lattice at $a\sim 0.12$ fm (or equivalently $a^{-1}\sim$1.67 GeV). Both valence and sea quarks are described by the overlap fermion formulation. The matching factor is calculated non-perturbatively ... More

Chiral perturbation theory in a theta vacuumJun 26 2009Mar 08 2010We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due to the CP violating term, the vacuum of chiral fields is shifted to a non-trivial element on the SU(N_f) group manifold. The CP violation also provides mixing of different CP ... More

Lattice Study of the Massive Schwinger Model with a $θ$ term under Lüscher's "Admissibility" conditionSep 16 2003Sep 18 2003We present a numerical study of the massive two-flavor QED in two dimensions with the gauge action proposed by L\"uscher, which allows only ``admissible'' gauge fields. We find that the admissibility condition does not allow any topology changes by the ... More

Finite volume scaling of the electro-magnetic pion form factor in the $ε$ regimeFeb 12 2014We consider finite volume effects on the electro-magnetic pion form factor near the chiral limit, in the so-called $\epsilon$ regime. The pseudoscalar-vector-pseudoscalar three-point function is calculated in the $\epsilon$ expansion of chiral perturbation ... More

Lattice Study of the Massive Schwinger Model with $θ$ Term under Lüscher's "Admissibility" ConditionMay 06 2003May 29 2003L\"uscher's ``admissibility'' condition on the gauge field space plays an essential role in constructing lattice gauge theories which has exact chiral symmetries. We apply the gauge action proposed by L\"uscher with the domain-wall fermion action to the ... More

Interpolation between the epsilon and p regimesMay 09 2011Jul 04 2011We reconsider chiral perturbation theory in a finite volume and develop a new computational scheme which smoothly interpolates the conventional epsilon and p regimes. The counting rule is kept essentially the same as in the p expansion. The zero-momentum ... More

Theta vacuum effects on the chiral condensation and the eta^prime meson correlators in the two-flavor massive QED_2 on the latticeMar 24 2004Apr 07 2004We study the scalar and pseudoscalar condensations and the eta^prime meson correlators of the two-flavor massive Schwinger model in the non-zero theta vacuum. Exploiting our new method which was developed to investigate topological effects in the previous ... More

Renormalization of Extended QCD$_2$Jul 09 2015Sep 10 2015Extended QCD (XQCD) proposed by Kaplan [1] is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low energy ... More

Extracting the electro-magnetic pion form factor from QCD in a finite volumeSep 01 2014We consider finite volume effects on the electromagnetic form factor of the pion. We compute the peudoscalar-vector-pseudoscalar correlator in the $\epsilon$ expansion of chiral perturbation theory up to the next-to-leading order and find a way to remove ... More

Lattice gauge action suppressing near-zero modes of H_WJul 16 2006Nov 08 2006We propose a lattice action including unphysical Wilson fermions with a negative mass m_0 of the order of the inverse lattice spacing. With this action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0) cannot appear and near-zero modes ... More

Lattice simulation of 2+1 flavors of overlap light quarksOct 15 2007We report on the status of the dynamical overlap QCD simulation project by the JLQCD collaboration. After completing two-flavor QCD simulation on a 16^3x32 lattice at lattice spacing a 0.12 fm, we started a series of runs with 2+1 flavors. In this report, ... More

Lattice study of meson correlators in the epsilon-regime of two-flavor QCDNov 30 2007Mar 05 2008We calculate mesonic two-point functions in the epsilon-regime of two-flavor QCD on the lattice with exact chiral symmetry. We use gauge configurations of size 16^3 32 at the lattice spacing a \sim 0.11 fm generated with dynamical overlap fermions. The ... More

B_K with dynamical overlap fermionsOct 02 2007We report on a calculation of $B_K$ with two-flavor dynamical overlap fermions on a $16^3 \times 32$ lattice at $a\sim 0.12$ fm. The results are compared with the PQChPT prediction of quark mass dependence. The systematic errors due to finite volume effects ... More

Dynamical overlap fermions in the epsilon-regimeOct 03 2006We report on the two-flavor QCD simulation in the epsilon-regime using the overlap fermion formulation. Sea quark mass is reduced to ~ 2 MeV on a 16^3x32 lattice with the lattice spacing ~ 0.11fm. Topological charge is fixed at Q=0. We compare the eigenvalue ... More

Determination of the chiral condensate from QCD Dirac spectrum on the latticeDec 18 2010Mar 01 2011We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~ 1.8-1.9 fm lattices ... More

Chiral behavior of kaon semileptonic form factors in lattice QCD with exact chiral symmetryNov 27 2012We calculate the kaon semileptonic form factors in lattice QCD with three flavors of dynamical overlap quarks. Gauge ensembles are generated at pion masses as low as 290 MeV and at a strange quark mass near its physical value. We precisely calculate relevant ... More

Kaon semileptonic form factors in QCD with exact chiral symmetryDec 22 2011We report on our calculation of the kaon semileptonic form factors in Nf=2+1 lattice QCD. Chiral symmetry is exactly preserved by using the overlap quark action for a straightforward comparison with chiral perturbation theory (ChPT). We simulate three ... More

Theta vacuum effects on the pseudoscalar condensates and the eta^prime meson in 2-dimensional lattice QEDSep 06 2004We study the chiral condensates and the eta^prime meson correlators of the massive Schwinger model in non-zero theta vacuum. Our data suggest that the pseudoscalar operator does condense in a fixed topological sector and gives long range correlations ... More

Renormalization of two-dimensional XQCDOct 15 2015Recently, Kaplan proposed an interesting extension of QCD named Extended QCD or XQCD with bosonic auxiliary fields [1]. While its partition function is kept exactly the same as that of QCD, XQCD naturally contains properties of low-energy hadrons. We ... More

Chiral behavior of light meson form factors in 2+1 flavor QCD with exact chiral symmetryJan 28 2016We present a study of chiral behavior of light meson form factors in QCD with three flavors of overlap quarks. Gauge ensembles are generated at single lattice spacing 0.12 fm with pion masses down to 300 MeV. The pion and kaon electromagnetic form factors ... More

Determination of the chiral condensate from 2+1-flavor lattice QCDNov 30 2009Sep 17 2010We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16^3x48 lattice at a lattice spacing around 0.11 fm. At ... More

Chiral properties of light mesons with $N_f=2+1$ overlap fermionsOct 29 2009We present an update of the light meson spectrum with $N_f$=2+1 overlap fermions on a $16^3\times 48$ lattice at five different up and down quark masses and two strange quark masses. Based on our experience with the previous simulation with $N_f=2$, we ... More

Pion vector and scalar form factors with dynamical overlap quarksOct 15 2008Oct 22 2008We calculate the pion vector and scalar form factors in two-flavor QCD. Gauge configurations are generated with dynamical overlap quarks on a 16^3 x 32 lattice at a lattice spacing of 0.12 fm with sea quark masses down to a sixth of the physical strange ... More

Topological susceptibility in 2-flavor lattice QCD with fixed topologyJun 11 2008We determine the topological susceptibility $ \chi_t $ in the trivial topological sector generated by lattice simulations of two-flavor QCD with overlap Dirac fermion, on a $16^3 \times 32$ lattice with lattice spacing $\sim$ 0.12 fm, at six sea quark ... More

Pion form factors from two-flavor lattice QCD with exact chiral symmetryMay 15 2009Oct 23 2009We calculate pion vector and scalar form factors in two-flavor lattice QCD and study the chiral behavior of the vector and scalar radii <r^2>_{V,S}. Numerical simulations are carried out on a 16^3 x 32 lattice at a lattice spacing of 0.12 fm with quark ... More

Light meson spectrum with $N_f=2+1$ dynamical overlap fermionsOct 08 2008We report on a numerical simulation with 2+1 dynamical flavors of overlap fermions. We calculate pseudo-scalar masses and decay constants on a $16^3\times 48 \times (0.11 {\rm fm})^4$ lattice at five different up and down quark masses and two strange ... More

Topological susceptibility in two-flavor lattice QCD with exact chiral symmetryOct 05 2007Jun 11 2008We determine the topological susceptibility $\chi_t$ in two-flavor QCD using the lattice simulations at a fixed topological sector. The topological charge density is unambiguously defined on the lattice using the overlap-Dirac operator which possesses ... More

Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetryJun 29 2008Aug 21 2008We calculate the nucleon sigma term in two-flavor lattice QCD utilizing the Feynman-Hellman theorem. Both sea and valence quarks are described by the overlap fermion formulation, which preserves exact chiral and flavor symmetries on the lattice. We analyse ... More

Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetryFeb 02 2007We perform lattice simulations of two-flavor QCD using Neuberger's overlap fermion, with which the exact chiral symmetry is realized at finite lattice spacings. The epsilon-regime is reached by decreasing the light quark mass down to 3 MeV on a 16^3 32 ... More

Mobility edge and locality of the overlap-Dirac operator with and without dynamical overlap fermionsSep 29 2006Oct 17 2006We perform a systematic study of low-lying eigenmodes of $H_w$ with various gauge actions to find the optimal choice for dynamical overlap fermion simulations, with which one may achieve lower numerical cost for HMC and better locality property of the ... More

Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix TheoryMay 23 2007Oct 28 2007The low-lying eigenvalue spectrum of the QCD Dirac operator in the epsilon-regime is expected to match with that of chiral Random Matrix Theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor QCD simulations ... More

The coarse Baum-Connes conjecture for relatively hyperbolic groupsSep 29 2011We study a group which is hyperbolic relative to a finite family of infinite subgroups. We show that the group satisfies the coarse Baum-Connes conjecture if each subgroup belonging to the family satisfies the coarse Baum-Connes conjecture and admits ... More

The coarse Baum-Connes conjecture for Busemann non-positively curved spacesApr 11 2013Oct 12 2014We prove that the coarse assembly maps for proper metric spaces which are non-positively curved in the sense of Busemann are isomorphisms, where we do not assume that the spaces are with bounded coarse geometry. Also it is shown that we can calculate ... More

Floer homology in symplectic geometry and in mirror symmetryJan 23 2006In this article, the authors review what the Floer homology is and what it does in symplectic geometry both in the closed string and in the open string context. In the first case, the authors will explain how the chain level Floer theory leads to the ... More

Flavor-singlet mesons in N_f=2+1 QCD with dynamical overlap quarksOct 24 2009We report on our study of flavor-singlet mesons in three-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated on a 16^3 x 48 lattice at a lattice spacing of 0.10 fm with the strange quark masses around its physical value m_s,phys and ... More

Coronae of product spaces and the Coarse Baum-Connes conjectureApr 10 2014We study the coarse Baum-Connes conjecture for product spaces and product groups. We show that a product of CAT(0) groups, polycyclic groups and relatively hyperbolic groups which satisfy some assumptions on peripheral subgroups, satisfies the coarse ... More

Coronae of relatively hyperbolic groups and coarse cohomologiesMar 08 2013Oct 08 2014We construct a corona of a relatively hyperbolic group by blowing-up all parabolic points of its Bowditch boundary. We relate the $K$-homology of the corona with the $K$-theory of the Roe algebra, via the coarse assembly map. We also establish a dual ... More

Convergence of the chiral expansion in two-flavor lattice QCDJun 05 2008Oct 27 2008We test the convergence property of the chiral perturbation theory (ChPT) using a lattice QCD calculation of pion mass and decay constant with two dynamical quark flavors. The lattice calculation is performed using the overlap fermion formulation, which ... More

Compactifications of S-arithmetic quotients for the projective general linear groupOct 03 2015Let F be a global field, and let S be a finite set of places of F containing all archimedean places. Consider the product X of the symmetric spaces and Bruhat-Tits buildings for PGL_d of the completions of F at archimedean and non-archimedean places in ... More

Homological algebra related to surfaces with boundaryAug 11 2015Jul 14 2016In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for ... More

1st or 2nd; the order of finite temperature phase transition of Nf=2 QCD from effective theory analysisDec 05 2013In the previous work, we have shown that the SU(2) chiral symmetry recovered above the critical temperature gives a strong constraint on the Dirac eigenvalue spectrum and this constraint is strong enough for a set of anomalous U(1) chiral symmetry breaking ... More

Chiral symmetry restoration and eigenvalue density of Dirac operatorDec 07 2012We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings to avoid possible ... More

Meson correlators in a finite volume near the chiral limitOct 07 2005We report on the results of our calculation of meson correlators in a finite volume. The calculation is carried out in the quenched approximation near the chiral limit (down to Mq = 2.6 MeV) using the overlap fermion. For these small quark masses, the ... More

Global Well-Posedness on a generalized derivative nonlinear Schrödinger equationOct 02 2016Oct 08 2016We prove global well-posedness for a generalized derivative nonlinear Schr\"odinger equation (gDNLS) by a variational argument. The variational argument is applicable to a cubic derivative nonlinear Schr\"odinger equation (DNLS). For (DNLS), Wu proved ... More

Exact Lagrangian submanifolds in simply-connected cotangent bundlesJan 26 2007Sep 13 2007We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) ... More

Low-lying mode contribution to the quenched meson correlators in the epsilon-regimeApr 22 2005Jun 01 2005We present a quenched calculation of meson correlators with the overlap fermion at very small masses 2.6--13 MeV. In this region the pion Compton wavelength is larger than our lattice size L\simeq 1.23fm and the system is in the so-called epsilon-regime ... More

Two-flavor QCD simulation with exact chiral symmetryMar 21 2008Jul 29 2008We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably ... More

JLQCD's dynamical overlap projectOct 05 2006We present an overview of our project of large-scale simulations with dynamical overlap fermions. The first production run in two-flavor QCD is on-going using the Iwasaki gauge action on a 16^3 \times 32 lattice at the lattice spacing of 0.12fm with six ... More

Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperatureSep 10 2012Apr 08 2013We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac operator, ... More

The symplectic geometry of cotangent bundles from a categorical viewpointMay 23 2007Sep 26 2007We describe various approaches to understanding Fukaya categories of cotangent bundles. All of the approaches rely on introducing a suitable class of noncompact Lagrangian submanifolds. We review the work of Nadler-Zaslow (math/0604379, math/0612399) ... More

Modular symbols and the integrality of zeta elementsJul 02 2015Feb 03 2016We consider modifications of Manin symbols in first homology groups of modular curves with p-adic integer coefficients for an odd prime p. We show that these symbols generate homology in primitive eigenspaces for the action of diamond operators, with ... More

Modular symbols in Iwasawa theoryFeb 16 2014Jan 05 2015This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author ... More