arXiv subjects
Publications and source records attributed to Hiroki Makino.
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then illustrate the Wilsonian RG flow on the basis of the gradient flow in two examples that possess an infrared fixed point, the 4D many-flavor gauge theory and the 3D $O(N)$ linear sigma model.
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.
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].
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.
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.
We give an alternative perturbative proof of the renormalizability of the system defined by the gradient flow and the fermion flow in vector-like gauge theories.
Recently, Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories on the basis of a chiral overlap operator. We compute the classical continuum limit of the fermion number anomaly in this formulation. Unexpectedly, we find that the continuum limit contains a term which is not Lorentz invariant. The term is, however, proportional to the gauge anomaly coefficient, and thus the fermion number anomaly in this lattice formulation automatically restores the Lorentz-invariant form when and only when the anomaly cancellation condition is met.
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.
We study the next-to-minimal supersymmetric standard model (NMSSM) with the TeV scale mirage mediation, which is known as a solution for the little hierarchy problem in supersymmetry. Our previous study showed that 125 GeV Higgs boson is realized with O(10) % fine-tuning for 1.5 TeV gluino (1 TeV stop) mass. The $μ$ term could be as large as 500 GeV without sacrificing the fine-tuning thanks to a cancellation mechanism. The singlet-doublet mixing is suppressed by $\tanβ$. In this paper, we further extend this analysis. We argue that approximate scale symmetries play a role behind the suppression of the singlet-doublet mixing. They reduce the mixing matrix to a simple form that is useful to understand the results of the numerical analysis. We perform a comprehensive analysis of the fine-tuning including the singlet sector by introducing a simple formula for the fine-tuning measure. This shows that the singlet mass of the least fine-tuning is favored by the LEP anomaly for moderate $\tanβ$. We also discuss prospects for the precision measurements of the Higgs couplings at LHC and ILC and direct/indirect dark matter searches in the model.
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.
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.
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.
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.
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.
We study the next-to-minimal supersymmetric standard model. We consider soft supersymmetry breaking parameters, which are induced by the mirage mediation mechanism of supersymmetry breaking. We concentrate on the mirage mediation, where the so-called mirage scale is the TeV scale. In this scenario, we can realize the up-type Higgs soft mass of O(200) GeV, while other masses such as gaugino masses and stop masses are heavy such as 1 TeV or more. Cancellation between the effective μ-term and the down-type Higgs soft mass ameliorates the fine-tuning in the electroweak symmetry breaking even for μ=O(500) GeV. The mixing between the doublet and singlet Higgs bosons is suppressed by (λ/κ)/tanβ. Then the lightest doublet Higgs mass naturally reaches 125 GeV lifted by the new quartic coupling. The higgsino and singlino are light and their linear combination is the lightest superparticle.