arXiv subjects

Hiroshi Suzuki

Publications and source records attributed to Hiroshi Suzuki.

At least 91 records · Page 5Linked to original sources

arXiv2015

Thermodynamics and reference scale of SU(3) gauge theory from gradient flow on fine lattices

We study the parametrization of lattice spacing and thermodynamics of SU(3) gauge theory on the basis of the Yang-Mills gradient flow on fine lattices. The lattice spacing of the Wilson gauge action is determined over a wide range $6.3\leβ\le7.5$ with high accuracy. The measurements of the flow time and lattice spacing dependences of the expectation values of the energy-momentum tensor are performed on fine lattices.

hep-lat↗

arXiv2015

(2+1)-flavor QCD Thermodynamics from the Gradient Flow

Recently, we proposed a novel method to define and calculate the energy-momentum tensor (EMT) in lattice gauge theory on the basis of the Yang-Mills gradient flow [1]. In this proceedings, we summarize the basic idea and technical steps to obtain the bulk thermodynamic quantities in lattice gauge theory using this method for the quenched and $(2+1)$-flavor QCD. The revised results of integration measure (trace anomaly) and entropy density of the quenched QCD with corrected coefficients are shown. Furthermore, we also show the flow time dependence of the parts of EMT including the dynamical fermions. This work is based on a joint-collaboration between FlowQCD and WHOT QCD.

hep-lat↗

arXiv2015

Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow

A parametrization of the lattice spacing ($a$) in terms of the bare coupling ($β$) for the SU(3) Yang--Mills theory with the Wilson gauge action is given in a wide range of~$β$. The Yang--Mills gradient flow with respect to the flow time~$t$ for the dimensionless observable, $t\frac{d}{dt}t^2\langle E(t)\rangle$, is utilized to determine the parametrization. With fine lattice spacings ($6.3\leβ\le7.5$) and large lattice volumes ($N_{\rm s}=64$--$128$), the discretization and finite-volume errors are significantly reduced to the same level as the statistical error.

hep-lat↗

arXiv2015

Complex Langevin method applied to the 2D $SU(2)$ Yang-Mills theory

The complex Langevin method in conjunction with the gauge cooling is applied to the two-dimensional lattice $SU(2)$ Yang-Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.

hep-lat↗

arXiv2015

Background field method in the gradient flow

In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom. In the present paper, we consider a modified form of the gauge-fixing term that manifestly preserves covariance under the background gauge transformation. It is shown that our gauge-fixing term does not affect gauge-invariant quantities as the conventional gauge-fixing term. The formulation thus allows a background gauge covariant perturbative expansion of the flow equation that provides, in particular, a very efficient computational method of expansion coefficients in the small flow time expansion. The formulation can be generalized to systems containing fermions.

hep-lat↗

arXiv2015

Thermodynamics of SU(3) Gauge Theory from Gradient Flow

A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed temperature are calculated directly on 32^3 x (6,8,10) lattices from the thermal average of the well-defined energy-momentum tensor (T_{mu nu}^R(x)) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t-dependence of the flowed data.

hep-lat↗

arXiv2015

Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields

Local products of fields deformed by the so-called Yang--Mills gradient flow become renormalized composite operators. This fact has been utilized to construct a correctly normalized conserved energy--momentum tensor in the lattice formulation of the pure Yang--Mills theory. In the present paper, this construction is further generalized for vector-like gauge theories containing fermions.

hep-lat↗

arXiv2015

Energy-momentum tensor from the Yang-Mills gradient flow

The product of gauge fields generated by the Yang-Mills gradient flow for positive flow times does not exhibit the coincidence-point singularity and a local product is thus independent of the regularization. Such a local product can furthermore be expanded by renormalized local operators at zero flow time with finite coefficients that are governed by renormalization group equations. Using these facts, we derive a formula that relates the small flow-time behavior of certain gauge-invariant local products and the correctly-normalized conserved energy-momentum tensor in the Yang-Mills theory. Our formula provides a possible method to compute the correlation functions of a well-defined energy-momentum tensor by using lattice regularization and Monte Carlo simulation.

hep-lat↗

arXiv2015

Large-$N$ limit of the gradient flow in the 2D $O(N)$ nonlinear sigma model

The gradient flow equation in the 2D $O(N)$ nonlinear sigma model with lattice regularization is solved in the leading order of the $1/N$ expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy--momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large-$N$ method. This analysis confirms that the above lattice energy--momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a non-perturbative mass gap.

hep-lat↗

arXiv2015

Bosonization in the path integral formulation

We establish the direct $d=2$ on-shell bosonization $ψ_{L}(x_{+})=e^{iξ(x_{+})}$ and $ψ_{R}^{\dagger}(x_{-})=e^{iξ(x_{-})}$ in path integral formulation by deriving the off-shell relations $ψ_{L}(x)ψ_{R}^{\dagger}(x)=\exp[iξ(x)]$ and $ψ_{R}(x)ψ_{L}^{\dagger}(x)=\exp[-iξ(x)]$. Similarly, the on-shell bosonization of the bosonic commuting spinor, $ϕ_{L}(x_{+})=ie^{-iξ(x_{+})}\partial^{+}e^{-iχ(x_{+})}$, $ϕ^{\dagger}_{R}(x_{-})=e^{-iξ(x_{-})-iχ(x_{-})}$ and $ϕ_{R}(x_{-})=ie^{iξ(x_{-})}\partial^{-}e^{+iχ(x_{-})}$, $ϕ^{\dagger}_{L}(x_{+})=e^{iξ(x_{+})+iχ(x_{+})}$, is established in path integral formulation by deriving the off-shell relations $ϕ_{L}(x)ϕ^{\dagger}_{R}(x)=ie^{-iξ(x)}\partial^{+}e^{-iχ(x)}$ and $ϕ_{R}(x)ϕ^{\dagger}_{L}(x)=ie^{iξ(x)}\partial^{-}e^{iχ(x)}$.

hep-th↗

arXiv2015

Universal formula for the energy--momentum tensor via a flow equation in the Gross--Neveu model

For the fermion field in the two-dimensional Gross--Neveu model, we introduce a flow equation that allows a simple $1/N$ expansion. By employing the $1/N$ expansion, we examine the validity of a universal formula for the energy--momentum tensor which is based on the small flow-time expansion. We confirm that the formula reproduces a correct normalization and the conservation law of the energy--momentum tensor by computing the translation Ward--Takahashi relation in the leading non-trivial order in the $1/N$ expansion. Also, we confirm that the expectation value at finite temperature correctly reproduces thermodynamic quantities. These observations support the validity of a similar construction of the energy--momentum tensor via the gradient/Wilson flow in lattice gauge theory.

hep-lat↗

arXiv2015

Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model

It is known that the gauge field and its composite operators evolved by the Yang--Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As application of the UV finiteness of the gradient flow, we construct the energy--momentum tensor in the lattice formulation of the $O(N)$ non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

hep-lat↗

arXiv2014

Measurement of thermodynamics using gradient flow

We analyze bulk thermodynamics and correlation functions of the energy-momentum tensor in pure Yang-Mills gauge theory using the energy-momentum tensor defined by the gradient flow and small flow time expansion. Our results on thermodynamic observables are consistent with those obtained by the conventional integral method. The analysis of the correlation function of total energy supports the energy conservation. It is also addressed that these analyses with gradient flow require less statistics compared with the previous methods. All these results suggest that the energy-momentum tensor can be successfully defined and observed on the lattice with moderate numerical costs with the gradient flow.

hep-lat↗

arXiv2014

Lattice energy-momentum tensor from the Yang-Mills gradient flow -- a simpler prescription

In a recent paper [arXiv:1403.4772], we gave a prescription how to construct a correctly-normalized conserved energy--momentum tensor in lattice gauge theory containing fermions, on the basis of the Yang--Mills gradient flow. In the present note, we give an almost identical but somewhat superior prescription with which one can simply set the fermion mass parameter in our formulation zero for the massless fermion. This feature will be useful in applying our formulation to theories in which the masslessness of the fermion is crucial, such as multi-flavor gauge theories with an infrared fixed point.

hep-lat↗

arXiv2013

Extraction of 3D field maps of magnetic multipoles from 2D surface measurements with applications to the optics calculations of the large-acceptance superconducting fragment separator BigRIPS

The fringing fields of magnets with large apertures and short lengths greatly affect ion-optical calculations. In particular, for a high magnetic field where the iron core becomes saturated, the effective lengths and shapes of the field distribution must be considered because they change with the excitation current. Precise measurement of the three-dimensional magnetic fields and the correct application of parameters in the ion-optical calculations are necessary. First we present a practical numerical method of extracting full 3D magnetic field maps of magnetic multipoles from 2D field measurements of the surface of a cylinder. Using this novel method we extracted the distributions along the beam axis for the coefficient of the first-order quadrupole component, which is the leading term of the quadrupole components in the multipole expansion of magnetic fields and proportional to the distance from the axis. Higher order components of the 3D magnetic field can be extracted from the leading term via recursion relations. The measurements were done for many excitation current values for the large-aperture superconducting triplet quadrupole magnets (STQs) in the BigRIPS fragment separator at the RIKEN Nishina Center RI Beam Factory. These distributions were parameterized using the Enge functions to fit the fringe field shapes at all excitation current values, so that unmeasured values are interpolated. The extracted distributions depend only on the position along the beam axis, and thus the measured three-dimensional field can easily be parameterized for ion-optical calculations. We implemented these parameters in the ion-optical calculation code COSY INFINITY and realized a first-order calculation that incorporates the effect of large and varying fringe fields more accurately. We applied the calculation to determine the excitation current settings of the STQs...

physics.acc-ph↗

arXiv2013

SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.

hep-th↗

arXiv2013

Remark on the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM

In a recent paper, arXiv:1209.2473 \cite{Suzuki:2012gi}, we presented a possible definition of the energy-momentum tensor in the lattice formulation of the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory, that is conserved in the quantum continuum limit. In the present Letter, we propose a quite similar but somewhat different definition of the energy-momentum tensor (that is also conserved in the continuum limit) which is superior in several aspects: In the continuum limit, the origin of the energy automatically becomes consistent with the supersymmetry and the number of renormalization constants that require a (non-perturbative) determination is reduced to two from four, the number of renormalization constants appearing in the construction in Ref. \cite{Suzuki:2012gi}.

hep-lat↗

arXiv2012

Ferrara--Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM

It is well-known that Noether currents in the classical four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory (4D $\mathcal{N}=1$ SYM), i.e., the $U(1)_A$ current, the supersymmetry (SUSY) current and the energy-momentum tensor, form a multiplet under SUSY, called the Ferrara--Zumino supermultiplet. Inspired by this structure, we define the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM by a renormalized super transformation of a lattice SUSY current. By using a renormalized SUSY Ward--Takahashi relation, the energy-momentum tensor so constructed is shown to be conserved in the quantum continuum limit. Our construction of the energy-momentum tensor is very explicit and usable in non-perturbative numerical simulations.

hep-lat↗