Daisuke Kadoh

A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

We correct the incomplete proof of the global integrability condition for non-gauge loops (the non-contractible loops along the Wilson-line degrees of freedom of U(1) gauge field) in JHEP05(2008)095. Accordingly, the reconstruction theorem is reformulated. The main result does not change.

A numerical solution to the local cohomology problem in U(1) chiral gauge theories

We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in {\rm U}(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincare lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties.

One dimensional supersymmetric Yang-Mills theory with 16 supercharges

We report on numerical simulations of one dimensional maximally supersymmetric SU(N) Yang-Mills theory, by using the lattice action with two exact supercharges. Based on the gauge/gravity duality, the gauge theory corresponds to N D0-branes system in type IIA superstring theory at finite temperature. We aim to verify the gauge/gravity duality numerically by comparing our results of the gauge side with analytic solutions of the gravity side. First of all, by examining the supersymmetric Ward-Takahashi relation, we show that supersymmetry breaking effects from the cut-off vanish in the continuum limit and our lattice theory has the desired continuum limit. Then, we find that, at low temperature, the black hole internal energy obtained from our data is close to the analytic solution of the gravity side. It suggests the validity of the duality.

A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in finite volume. The resulted formula is very close to the known expression of the measure term in infinite volume with a single parameter integration, and would be useful in practical implementations.

Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

In the gauge-invariant construction of abelian chiral gauge theories on the lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topological and its cohomologically trivial part plays the role of the local counter term. We give a prescription to solve the local cohomology problem within a finite lattice by reformulating the Poincare lemma so that it holds true on the finite lattice up to exponentially small corrections. We then argue that the path-integral measure of Weyl fermions can be constructed directly from the quantities defined on the finite lattice.

Light hadron spectrum with 2+1 flavor dynamical O(a)-improved Wilson quarks

We present preliminary results for the light harden spectrum in N f = 2 + 1 lattice QCD using the nonperturbatively O(a)-improved Wilson quark action and the Iwasaki gauge action. Simulations are carried out at β = 1.90 on a 32 3 × 64 lattice using the PACS-CS computer. We employ Luscher’s domain-decomposed HMC algorithm to reduce the up-down quark masses toward the physical value. The pseudoscalar meson masses range from 730 MeV down to 210 MeV. We compare the light harden spectrum extrapolated to the physical point with the experimental values.

Application of chiral perturbation theory to 2+1 flavor lattice QCD with O(a)-improved Wilson quarks

We apply chiral perturbation theory to the pseudoscalar meson mass and decay constant data obtained in the PACS-CS Project toward 2+1 flavor lattice QCD simulations with the O(a)-improved Wilson quarks. We examine the existence of chiral logarithms in the quark mass range from m_{ud}=47 MeV down to 6 MeV on a (2.8 fm)^3 box with the lattice spacing a=0.09 fm. Several low energy constants are determined. We also discuss the magnitude of finite size effects based on chiral perturbation theory.

Recent progress in lattice supersymmetry: from lattice gauge theory to black holes

Supersymmetry (SUSY) is a fascinating topic in theoretical physics, because of its unique and counterintuitive properties. It is expected to emerge as new physics beyond the standard model, and it is also a building block for supergravity and superstring theory. A number of exact results obtained via SUSY theories provide insights into field theory. However, the dynamics of many SUSY theories are not yet fully understood, and numerical study of SUSY theories through lattice simulations is promising as regards furthering this understanding. In this paper, I overview the current status of lattice SUSY by discussing its development in chronological order, and by reviewing some simple models. In addition, I discuss the numerical verification of gauge/gravity duality, which is one of the recent significant developments in this field.

Precision test of the gauge/gravity duality in two-dimensional N=(8,8) SYM

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Application of tensor network method to two dimensional lattice N = 1 Wess–Zumino model

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