Realizing three generations of the Standard Model fermions in the type IIB matrix model

We discuss how the Standard Model particles appear from the type IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. In particular, we are concerned with a constructive definition of the theory, in which we start with finite-N matrices and take the large-N limit afterwards. In that case, it was pointed out recently that realizing chiral fermions in the model is more difficult than it had been thought from formal arguments at N=infinity and that introduction of a matrix version of the warp factor is necessary. Based on this new insight, we show that two generations of the Standard Model fermions can be realized by considering a rather generic configuration of fuzzy S^2 and fuzzy S^2 * S^2 in the extra dimensions. We also show that three generations can be obtained by squashing one of the S^2's that appear in the configuration. Chiral fermions appear at the intersections of the fuzzy manifolds with nontrivial Yukawa couplings to the Higgs field, which can be calculated from the overlap of their wave functions.Comment: 28 pages, 11 figures; (v2) references added, typos corrected; (v3) footnote added, version to be published on JHE

The Effect of Dynamical Gauge Field on the Chiral Fermion on a boundary

We study the effect of dynamical gauge field on the Kaplan's chiral fermion on a boundary in the strong gauge coupling limit in the extra dimension. To all orders of the hopping parameter expansion, we prove exact parity invariance of the fermion propagator on the boundary. This means that the chiral property of the boundary fermion, which seems to survive even in the presence of the gauge field from a perturbative point of view, is completely destroyed by the dynamics of the gauge field.Comment: 16 pages (including 7 figures), LaTeX, UT-675, KEK-TH-39

EIGENVALUE EXPRESSION FOR A BATCH MARKOVIAN ARRIVAL PROCESS

Abstract Consider a batch Markovian arrival process (BMAP) as the counting process of an underlying Markov process representing the state of environment. Such a process is useful for representing correlated inputs for example. They are used both as a modeling tool and as a theoretical device to represent and approximate superposition of input processes and complex large systems. Our objective is to consider the first and second moments of the counting process depending on time and state. Assuming that the probability generating functions of batch size are analytic, and that eigenvalues of the infinitesimal generator are simple, we derive an analytic diagonalization for the matrix generating function of the counting process. Our main result gives the time-dependent form of the first and second factorial moments of the counting process, which is represented by eigenvalues and eigenvectors of the matrix generating function of the batch size. 1

民間利用に向けた研究データのデータポリシーの提案

第5回オープンサイエンスデータ推進ワークショップ -データマネージメントの実施および教育の現状報告を中心に-（2018年3月1-2日, 京都大学理学研究科セミナーハウス

Orbifold Matrix Model

We study a matrix model describing type IIB superstring in orbifold backgrounds. We particularly consider a {\bf C}^3/{\bf Z}_3 orbifold model whose six dimensional transverse space is orbifolded by {\bf Z}_3 discrete symmetry. This model is chiral and has d=4 {\cal N}=1 supersymmetry of Yang-Mills type as well as an inhomogeneous supersymmetry specific to matrix models. We calculate one-loop effective action around some backgrounds, and the result can be interpreted as interactions mediated by massless particles in IIB supergravity in orbifold background, if the background is in the Higgs branch. If the background is in the Coulomb branch, the dynamics is governed by the reduced model of d=4 super Yang-Mills theory, which might be interpreted as exchange of massless particles in the twisted sector. But the perturbative calculation cannot reproduce the supergravity result. We also show that this model with a large Higgs vacuum expectation value becomes IIB (IKKT) matrix model.Comment: 23 pages, references adde

Effective colloidal processing for densification before SPS

In conventional dry processing, fine particles tend to agglomerate spontaneously due to Van der Waals attractive forces. Since the agglomeration of particles forms large residual pores in green bodies, elevated temperatures are necessary for densification. Colloidal processing is a very effective technique for controlling the pore size distribution in green compacts before sintering. The green compacts having small residual pores with a narrow size distribution is expected to enhance the densification at low sintering temperature during SPS. We already reported that colloidal processing for controlling the packing structure in green compact is effective for densification in SPS in the case of SiC. A commercially available SiC (6H) powder with the average particle size of 0.55 mm was used as the starting materials. When using the dry processing for consolidation, the density of the sample sintered by SPS in a vacuum atmosphere at 1950°C was 92% of the theoretical value. Aqueous suspensions with dispersed particles were prepared by adjusting pH and consolidated by slip casting to prepare the dense green compacts. The relative density of SiC prepared by SPS was increased with increasing temperature and reached more than 97% at 1950°C as shown in Fig. 1. In this presentation, this processing was applied to fabrication of transparent alumina. Commercially available Al2O3 powder with the average particle size of 0.4 mm was used as the starting materials. Suspensions with 30 vol% solid were consolidated by slip casting. The green compacts before sintering were further densified by cold isostatic pressing at 392 MPa for 10 min and calcined at 500°C for 1 h in air in order to burn off the dispersant. Final sintering was carried out at 1150°C under a uniaxial pressure of 100 MPa using an SPS. After rapid heating to 600°C, the temperature was raised from 600°C to 1150°C using a heating rate of 5°C/min. After holding samples at the sintering temperature for 10 min and then subsequently annealing them at 1000°C for 10 min, we obtained a sintered disk with a diameter of 25 mm and a thickness of 2 mm. Fig. 2(a) shows the photograph of the sample from the green compact prepared by slip casting, Fig2(b) is the sample densified by SPS from the as-received powder directly. The transparency of the sample prepared by slip casting is clearer than that of the sample by SPS from the as-received powder directly. Please click Additional Files below to see the full abstract

Dynamical generation of a nontrivial index on the fuzzy 2-sphere

In the previous paper hep-th/0312199 we studied the 't Hooft-Polyakov (TP) monopole configuration in the U(2) gauge theory on the fuzzy 2-sphere and showed that it has a nonzero topological charge in the formalism based on the Ginsparg-Wilson relation. In this paper, by showing that the TP monopole configuration is stabler than the U(2) gauge theory without any condensation in the Yang-Mills-Chern-Simons matrix model, we will present a mechanism for dynamical generation of a nontrivial index. We further analyze the instability and decay processes of the U(2) gauge theory and the TP monopole configuration.Comment: Latex2e, 30 pages, 4 figures, the topological charge for a monopole configuration is corrected, reference added, the final version to appear in Physical Review D (the typos mentioned in the erratum are corrected

Dominance of a single topological sector in gauge theory on non-commutative geometry

We demonstrate a striking effect of non-commutative (NC) geometry on topological properties of gauge theory by Monte Carlo simulations. We study 2d U(1) NC gauge theory for various boundary conditions using a new finite-matrix formulation proposed recently. We find that a single topological sector dictated by the boundary condition dominates in the continuum limit. This is in sharp contrast to the results in commutative space-time based on lattice gauge theory, where all topological sectors appear with certain weights in the continuum limit. We discuss possible implications of this effect in the context of string theory compactifications and in field theory contexts.Comment: 16 pages, 27 figures, typos correcte