Related papers: Geometric General Solution to the $U(1)$ Anomaly E…
The exact operator solutions of two-dimensional anomaly-free chiral abelian gauge theories are obtained. We show that anomaly-cancellation conditions arise as consistency requirements of these solutions. For a certain class of flavour…
We report the most general expression for the chiral charges of a non-universal $U(1)'$ with identical charges for the first two families but different charges for the third one. The model is minimal in the sense that only standard model…
We reconsider models of fermion masses and mixings based on a gauge anomalous horizontal U(1) symmetry. In the simplest model with a single flavon field and horizontal charges of the same sign for all Standard Model fields, only very few…
We propose a mechanism which explains the masses of $\eta$ and $\eta'$ mesons without invoking the explicit violation of $U(1)_A$ symmetry by the chiral anomaly. It is shown that the U(1) problem, the problem for which the prediction of…
We show that conventional asymmetric chiral random matrix models (ChRMM), with a gaussian distribution in the asymmetry, provide for a screening of the topological charge and a resolution of the $U(1)$ problem in the unquenched…
There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance ("fermion number"). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers…
We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then…
The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge…
We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work…
We review the status of our recent work on the gauge-fixing approach to lattice chiral gauge theories. New numerical results in the reduced version of a model with a U(1) gauge symmetry are presented which strongly indicate that the…
It is well-known that the charge of fermion is 0 or $\pm1$ in the U(1) gauge theory on noncommutative spacetime. Since the deviation from the standard model in particle physics has not yet observed, and so there may be no room to…
We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a…
Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…
In this talk, we introduce a new scenario of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry. Since generic interactions (including non-renormalizable interactions) are introduced, once we fix the symmetry of the theory,…
We consider a theory with gauge group $G \times U(1)_A$ containing: i) an abelian factor for which the chiral matter content of the theory is anomalous $\sum_{f} q^f_A \neq 0 \neq \sum_{f} (q^f_A)^3$ ; ii) a nonanomalous factor $G$. In…
After discussing the problem of lattice regularization of chiral gauge theories, a simple model for anomalous fermion number violation is formulated which can be numerically studied with present day technique. Exploratory results of…
The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…
We use algebraic geometry to study the anomaly-free representations of an arbitrary gauge Lie algebra for 4-dimensional spacetime fermions. For irreducible representations, the problem reduces to studying the Lie algebras $\mathfrak{su}_n$…
Using the method of finite differences a scheme is proposed to solve exactly the Klein-Gordon and Dirac free field equations, in a (1+1)-dimensional lattice. The hamiltonian of the Dirac field is translational invariant, hermitian, avoids…
I discuss supersymmetric extensions of the Standard Model containing an extra U(1)' gauge symmetry which provide a solution to the mu-problem and at the same time protect the proton from decaying via dimension 4 operators. Moreover, all…