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Hiroshi Suzuki

Publications and source records attributed to Hiroshi Suzuki.

At least 73 records · Page 4Linked to original sources
arXiv2018

4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow

The gradient flow and its small flow-time expansion provide a very versatile method to represent renormalized composite operators in a regularization-independent manner. This technique has been utilized to construct typical Noether currents such as the energy--momentum tensor and the axial-vector current in lattice gauge theory. In this paper, we apply the same technique to the supercurrent in the four-dimensional $\mathcal{N}=1$ super Yang--Mills theory (4D $\mathcal{N}=1$ SYM) in the Wess--Zumino gauge. Since this approach provides a priori a representation of the properly normalized conserved supercurrent, our result should be useful, e.g., in lattice numerical simulations of the 4D $\mathcal{N}=1$ SYM; the conservation of the so-constructed supercurrent can be used as a criterion for the supersymmetric point toward which the gluino mass is tuned.

hep-lat↗
arXiv2018

Axial $U(1)$ anomaly in a gravitational field via the gradient flow

A regularization-independent universal formula for the energy--momentum tensor in gauge theory in the flat spacetime can be written down by employing the so-called Yang--Mills gradient flow. We examine a possible use of the formula in the calculation of the axial $U(1)$ anomaly in a gravitational field, the anomaly first obtained by Toshiei Kimura [Prog.\ Theor.\ Phys.\ {\bf 42}, 1191 (1969)]. As a general argument indicates, the formula reproduces the correct non-local structure of the (axial $U(1)$ current)--(energy--momentum tensor)--(energy--momentum tensor) triangle diagram in a way that is consistent with the axial $U(1)$ anomaly. On the other hand, the formula does not automatically reproduce the general coordinate (or translation) Ward--Takahashi relation, requiring corrections by local counterterms. This analysis thus illustrates the fact that the universal formula as it stands can be used only in on-shell correlation functions, in which the energy--momentum tensor does not coincide with other composite operators in coordinate space.

hep-th↗
arXiv2017

Energy-momentum tensor correlation function in Nf=2+1 full QCD at finite temperature

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in $N_f=2+1$ full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturbatively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing $=0.07$ fm. In this paper the temperature is limited to a single value $T=232$ MeV. The $u$, $d$ quark mass is rather heavy with $m_π/m_ρ=0.63$ while the $s$ quark mass is set to approximately its physical value.

hep-lat↗
arXiv2017

Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow

We study the energy-momentum tensor and the equation of state as well as the chiral condensate in (2+1)-flavor QCD at the physical point applying the method of Makino and Suzuki based on the gradient flow. We adopt a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. At Lattice 2016, we have presented our preliminary results of our study in (2+1)-flavor QCD at a heavy u, d quark mass point. We now extend the study to the physical point and perform finite-temperature simulations in the range T \simeq 155--544 MeV (Nt = 4--14 including odd Nt's) at a \simeq 0.09 fm. We show our final results of the heavy QCD study and present some preliminary results obtained at the physical point so far.

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arXiv2017

4D $\mathcal{N}=1$ SYM supercurrent on the lattice in terms of the gradient flow

The gradient flow[1-5] gives rise to a versatile method to construct renormalized composite operators in a regularization-independent manner. By adopting this method, the authors of~Refs.[6-9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D $\mathcal{N}=1$ super Yang--Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess--Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields[10].

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arXiv2017

One-loop perturbative coupling of $A$ and $A_\star$ through the chiral overlap operator

Recently, Grabowska and Kaplan constructed a four-dimensional lattice formulation of chiral gauge theories on the basis of the chiral overlap operator. At least in the tree-level approximation, the left-handed fermion is coupled only to the original gauge field~$A$, while the right-handed one is coupled only to the gauge field~$A_\star$, a deformation of~$A$ by the gradient flow with infinite flow time. In this paper, we study the fermion one-loop effective action in their formulation. We show that the continuum limit of this effective action contains local interaction terms between $A$ and~$A_\star$, even if the anomaly cancellation condition is met. These non-vanishing terms would lead an undesired perturbative spectrum in the formulation.

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arXiv2017

Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow

We compute the topological charge and its susceptibility in finite temperature (2+1)-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson quarks, we perform simulations on a fine lattice with~$a\simeq0.07\,\mathrm{fm}$ at a heavy $u$, $d$ quark mass with $m_π/m_ρ\simeq0.63$ but approximately physical $s$ quark mass with $m_{η_{ss}}/m_ϕ\simeq0.74$. In a temperature range from~$T\simeq174\,\mathrm{MeV}$ ($N_t=16$) to $697\,\mathrm{MeV}$ ($N_t=4$), we study two topics on the topological susceptibility. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Because the two definitions are related by chiral Ward-Takahashi identities, their equivalence is not trivial for lattice quarks which violate the chiral symmetry explicitly at finite lattice spacings. The gradient flow method enables us to compute them without being bothered by the chiral violation. We find a good agreement between the two definitions with Wilson quarks. The other is a comparison with a prediction of the dilute instanton gas approximation, which is relevant in a study of axions as a candidate of the dark matter in the evolution of the Universe. We find that the topological susceptibility shows a decrease in $T$ which is consistent with the predicted $χ_\mathrm{t}(T) \propto (T/T_{\rm pc})^{-8}$ for three-flavor QCD even at low temperature $T_{\rm pc} < T\le1.5 T_{\rm pc}$.

hep-lat↗
arXiv2017

A dilaton-pion mass relation

Recently, Golterman and Shamir presented an effective field theory which is supposed to describe the low-energy physics of the pion and the dilaton in an $SU(N_c)$ gauge theory with $N_f$ Dirac fermions in the fundamental representation. By employing this formulation with a slight but important modification, we derive a relation between the dilaton mass squared~$m_τ^2$, with and without the fermion mass~$m$, and the pion mass squared~$m_π^2$ to the leading order of the chiral logarithm. This is analogous to a similar relation obtained by Matsuzaki and~Yamawaki on the basis of a somewhat different low-energy effective field theory. Our relation reads $m_τ^2=m_τ^2|_{m=0}+KN_f\hat{f}_π^2m_π^2/(2\hat{f}_τ^2)+O(m_π^4\ln m_π^2)$ with~$K=9$, where $\hat{f}_π$ and~$\hat{f}_τ$ are decay constants of the pion and the dilaton, respectively. This mass relation differs from the one derived by Matsuzaki and~Yamawaki on the points that $K=(3-γ_m)(1+γ_m)$, where $γ_m$ is the mass anomalous dimension, and the leading chiral logarithm correction is~$O(m_π^2\ln m_π^2)$. For~$γ_m\sim1$, the value of the decay constant~$\hat{f}_τ$ estimated from our mass relation becomes $\sim50\%$ larger than $\hat{f}_τ$ estimated from the relation of Matsuzaki and~Yamawaki.

hep-lat↗
arXiv2017

One-loop perturbative coupling of $A$ and $A_\star$ through the chiral overlap operator

We study the one-loop effective action defined by the chiral overlap operator in the four-dimensional lattice formulation of chiral gauge theories by Grabowska and Kaplan. In the tree-level continuum limit, the left-handed component of the fermion is coupled only to the original gauge field~$A$, while the right-handed one is coupled only to~$A_\star$, which is given by the gradient flow of~$A$ with infinite flow time. In this paper, we show that the continuum limit of the one-loop effective action contains local interaction terms between $A$ and~$A_\star$, which do not generally vanish even if the gauge representation of the fermion is anomaly free. We argue that the presence of such interaction terms can be regarded as undesired gauge symmetry-breaking effects in the formulation.

hep-lat↗
arXiv2017

Energy--momentum tensor on the lattice: recent developments

It is conceivable that the construction of the energy--momentum tensor (EMT) in lattice field theory enlarges our ability in lattice field theory and also deepens our understanding on EMT at the non-pertubative level. In this talk, I will review recent developments in this enterprise.

hep-lat↗
arXiv2017

Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow

The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with $β=6.287$--$7.500$ corresponding to the lattice spacing $a= 0.013$--$0.061\,\mathrm{fm}$. The spatial (temporal) sizes are chosen to be $N_s= 64$, $96$, $128$ ($N_τ=12$, $16$, $20$, $22$, $24$) with the aspect ratio, $5.33 \le N_s/N_τ \le 8$. Double extrapolation, $a\rightarrow 0$ (the continuum limit) followed by $t\rightarrow 0$ (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.

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arXiv2017

Determination of latent heat at the finite temperature phase transition of SU(3) gauge theory

We calculate the energy gap (latent heat) and pressure gap between the hot and cold phases of the SU(3) gauge theory at the first order deconfining phase transition point. We perform simulations around the phase transition point with the lattice size in the temporal direction $N_t=6,$ 8 and 12 and extrapolate the results to the continuum limit. The energy density and pressure are evaluated by the derivative method with nonperturabative anisotropy coefficients. We find that the pressure gap vanishes at all values of $N_t$. The spatial volume dependence in the latent heat is found to be small on large lattices. Performing extrapolation to the continuum limit, we obtain $Δε/T^4 = 0.75 \pm 0.17$ and $Δ(ε-3 p)/T^4 = 0.623 \pm 0.056.$ We also tested a method using the Yang-Mills gradient flow. The preliminary results are consistent with those by the derivative method within the error.

hep-lat↗
arXiv2016

Fermion number anomaly with the fluffy mirror fermion

Quite recently, Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator. We study this formulation from the perspective of the fermion number anomaly and possible associated phenomenology. A simple argument shows that the consistency of the formulation implies that the fermion with the opposite chirality to the physical one, the "fluffy mirror fermion" or "fluff", suffers from the fermion number anomaly in the same magnitude (with the opposite sign) as the physical fermion. This immediately shows that if at least one of the fluff quarks is massless, the formulation provides a simple viable solution to the strong CP problem. Also, if the fluff interacts with gravity essentially in the same way as the physical fermion, the formulation can realize the asymmetric dark matter scenario.

hep-lat↗
arXiv2016

Temperature dependence of topological susceptibility using gradient flow

We study temperature dependence of the topological susceptibility with the $N_{f}=2+1$ flavors Wilson fermion. We have two major interests in this paper. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Two definitions are related by the chiral Ward-Takahashi identity but their coincidence is highly non-trivial for the Wilson fermion. By applying the gradient flow both for the gauge and quark fields we find a good agreement of these two measurements. The other is a verification of a prediction of the dilute instanton gas approximation at low temperature region $T_{pc}< T<1.5T_{pc}$, for which we confirm the prediction that the topological susceptibility decays with power $χ_{t}\propto(T/T_{pc})^{-8}$ for three flavors QCD.

hep-lat↗
arXiv2016

Equation of state in (2+1)-flavor QCD with gradient flow

The energy-momentum tensor and equation of state are studied in finite-temperature (2+1)-flavor QCD with improved Wilson quarks using the method proposed by Makino and Suzuki based on the gradient flow. We find that the results of the gradient flow are consistent with the previous results using the $T$-integration method at $T \mathrel{\rlap{\raise 0.511ex \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}} 280$ MeV ($N_t\mathrel{\rlap{\raise 0.511ex \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}}10$), while a disagreement is found at $T \mathrel{\rlap{\raise 0.511ex \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}} 350$ MeV ($N_t \mathrel{\rlap{\raise 0.511ex \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}} 8$) presumably due to the small-$N_t$ lattice artifact. We also report on the results on the renormalized chiral condensate and its disconnected susceptibility using the method of Hieda and Suzuki. The results show a clear signal of the expected chiral restoration crossover even with Wilson-type quarks which violate the chiral symmetry explicitly.

hep-lat↗
arXiv2016

Background field method in the gradient flow

The Yang--Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non-perturbative regularization such as lattice. The gradient flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in perturbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transformation, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is relevant to the construction of a lattice energy--momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.

hep-lat↗
arXiv2016

Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach

We study four-dimensional conformal field theories with an $SU(N)$ global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin~$0$ operator~$ϕ_i^{\Bar{k}}$ which belongs to the adjoint representation of $SU(N)$. For~$N=12$ for example, we found that the theory contains a spin~$0$ $SU(12)$-breaking relevant operator when the scaling dimension of~$ϕ_i^{\Bar{k}}$, $Δ_{ϕ_i^{\Bar{k}}}$, is smaller than~$1.71$. Considering the lattice simulation of many-flavor quantum chromodynamics with $12$~flavors on the basis of the staggered fermion, the above $SU(12)$-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above $SU(12)$-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point~$γ_m^*\leq1.29$ from the relation~$γ_m^*=3-Δ_{ϕ_i^{\Bar{k}}}$. Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another $SU(12)$-breaking operator.

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