Related papers: Matrix model and Yukawa couplings on the noncommut…
The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry.…
As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace,…
We present a composite model that is based on non-perturbative effects of N=1 supersymmetric SU(N_C) gauge theory with N_f=N_C+1 flavors. In this model, we consider N_C=7, where all matter fields in the supersymmetric standard model, that…
It is suggested to combine gauge and Yukawa interactions into one expression involving the generalized Dirac operator associated with a superconnection $D+L$, $L$ being linked to the Higgs field (one doublet). We advocate a version of the…
We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our…
We study compactifications of Matrix theory on twisted tori and non-commutative versions of them. As a first step, we review the construction of multidimensional twisted tori realized as nilmanifolds based on certain nilpotent Lie algebras.…
We compute Yukawa couplings in type IIa string theory compactified on a six-torus in the presence of intersecting D6-branes. The six-torus is generated by an SO(12) root lattice. Yukawa couplings are expressed as sums over worldsheet…
We study the impacts of matter field K\"ahler metric on physical Yukawa couplings in string compactifications. Since the K\"ahler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
We discuss the propagation of fermions on generic, curved branes in IKKT-type matrix models. The Dirac operator can be understood either in terms of a Weitzenb\"ock connection, or in terms of the Levi-Civita connection with extra torsion…
We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and…
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…
In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in $\mathbb{S}^3$ (and $\mathbb{R}^3$) by Dirac operators with smooth magnetic fields. We then proceed to prove that under certain…
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a…
It is shown that the nonlocal Dirac operator yielded by a lattice model that preserves chiral symmetry and uniqueness of fields, approaches to an ultralocal and invariant under translations operator when the size of the lattice tends to…
Non-perturbative superpotential cross-couplings between visible sector matter and K\"ahler moduli can lead to significant flavour-changing neutral currents in compactifications of type IIB string theory. Here, we compute corrections to…
We discuss how unification of the gauge, Higgs and (three chiral family) matter superfields can be realized from the compactification of a six dimensional supersymmetric SU(8) gauge theory over the orbifold R^4 x T^2/Z_3. The bulk gauge…
We study non-linear $\sigma$-models defined on noncommutative torus as a two dimensional string world-sheet. We consider a quantum group as a noncommutative space-time as well as two points, a circle, and a noncommutative torus. Using the…
Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors…