Related papers: Finite flavour groups of fermions
The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.
We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional…
In this work we will investigate Lagrangians of the standard model extended by three right-handed neutrinos, and the consequences of invariance under finite groups G for lepton masses and mixing matrices are studied. The main part of this…
We construct a supersymmetric theory of flavor based on the discrete gauge group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one…
I discuss a new Physics scenario, the 331 model, based on the gauge group $SU(3)_c \times SU(3)_L \times U(1)_X$. In particular, I elaborate on correlations between flavour observables in the $B_d$ and $B_s$ systems that can help…
We classify the possible finite symmetries of conformal field theories with an affine Lie algebra su(2) and su(3), and discuss the results from the perspective of the graphs associated with the modular invariants. The highlights of the…
For any finite group Q not of prime power order, we construct a group G that is virtually of type F, contains infinitely many conjugacy classes of subgroups isomorphic to Q, and contains only finitely many conjugacy classes of other finite…
The origin of fermion mass hierarchies and mixings is one of the unresolved and most difficult problem in high-energy physics. One possibility to address the flavour problem is by extending the Standard Model to include a family symmetry.…
Groups of finite type (also called finitely constrained groups), introduced by Grigorchuk, are known to be the closure of regular branch groups. This article explores many of their properties. Firstly, we prove that being finitely…
The flavour puzzle is an open problem both in the Standard Model and in its possible supersymmetric or grand unified extensions. In this thesis, we discuss possible explanations of the origin of fermion mass hierarchies and mixings by the…
In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.
By an $\ell$-group $G$ we mean a lattice-ordered abelian group. This paper is concerned with the category $\FP$ of finitely presented {\it unital} $\ell$-groups, those $\ell$-groups having a distinguished order-unit $u$. Using the duality…
In this review article, we highlight the impact of models incorporating flavour symmetries on charged lepton flavour violating (LFV) processes. Flavour symmetries provide a natural approach to explain the peculiar mass hierarchies and…
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated…
In spite of the enormous success of the Standard Model (SM), we have strong reasons to expect the presence of new physics beyond the SM at higher energies. The idea of the Grand Unification of all the known interactions in nature is perhaps…
We summarize our investigations of several aspects of $\mathcal{N}=1$ supersymmetric Yang-Mills (SYM) theory. We present our final results for SU(3) $\mathcal{N}=1$ SYM simulated with Wilson fermions. We also discuss the first test of the…
Gauge theories with fermions in adjoint and fundamental representations are relevant for many different applications including composite Higgs models and general aspects of the confinement problem. We present first results from simulations…
Flavour symmetries in the dark sector are a theoretically motivated and phenomenologically appealing concept. The dark matter particle can be stabilised with the help of flavour symmetries, without the need to introduce an additional…
We extend Zirnbauer's color-flavor transformation in the fermionic sector to the case of the special unitary group. The transformation allows a certain integral over SU(N_c) color matrices to be transformed into an integral over flavor…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…