Phenomenological studies in the matrix models

Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability distribution of their appearance. This article mainly addresses studies in toroidal compactifications with magnetic fluxes.Comment: 5 pages; contribution to the proceedings of the Workshop on Noncommutative Field Theory and Gravity, Corfu, Greece, September 8-15, 2013; to appear in Fortsch. Phy

Chiral Fermions and the Standard Model from the Matrix Model Compactified on a Torus

It is shown that the IIB matrix model compactified on a six-dimensional torus with a nontrivial topology can provide chiral fermions and matter content close to the standard model on our four-dimensional spacetime. In particular, generation number three is given by the Dirac index on the torus.Comment: 21 pages, 5 figures; ver2: version published in Prog. Theor. Phys; ver3: minor correction

Index Theorem in Finite Noncommutative Geometry

Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological aspects in gauge theory is also shown.Comment: Latex 4 pages, uses ptptex.cls, Based on talk given at 21st Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics: Noncommutative Geometry and Quantum Spacetime in Physics, Japan, 11-15 Nov 200

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

Hofstadter butterflies for flat bands

Hofstadter's diagram, or the energy spectrum against the magnetic field in tight-binding systems, is obtained for the models having flat (dispersionless) one-electron band(s) that have originally been proposed for itinerant spin ferromagnetism. Magnetic fields preserve those flat bands that arise from a topological reason, while dispersions emerge in a singular manner for the flat bands arising from interference, implying an anomalous orbital magnetism.Comment: 9 pages, revtex, 4 figures available on request from [email protected]