Related papers: Discrete Anomalies of Binary Groups

Assuming that finite family symmetries are gauged, we derive discrete anomaly conditions for various non-Abelian groups. We thus provide new constraints for flavor model building, in which discrete non-Abelian symmetries are employed to…

We extend the well-known 't Hooft anomaly matching conditions for continuous global symmetries to discrete groups. We state the matching conditions for all possible anomalies which involve discrete symmetries explicitly. There are two types…

Beyond Standard Model physics frequently connects flavor symmetry with a discrete group. If the discrete symmetry arises spontaneously from a gauge theory, one can maintain compatibility with quantum gravity and avoid anomalies. We provide…

We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU(2) or SU(3) through spontaneous symmetry breaking. We consider all possible cases, where the…

We show that the discrete anomaly constraints governing popular non-Abelian symmetries of use in (e.g.) flavoured, supersymmetric, and dark matter model building typically subdivide into two classes differentiated by the simple restrictions…

In order to explain the fermions masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-abelian subgroup of $U(3)$ is added to the gauge group…

We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer…

Extra dimension deconstructed on a closed chain has naturally the symmetry of a regular polygon, the dihedral symmetry D_N. We assume that the fields are irreducible representations of the binary dihedral group Q_2N, which is the covering…

We consider group orders and right-orders which are discrete, meaning there is a least element which is greater than the identity. We note that free groups cannot be given discrete orders, although they do have right-orders which are…

The use of nonabelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g = 31, the most appealing candidates are two subgroups of SU(2): the dicyclic [double dihedral] group G = $Q_6 ={…

A nonabelian finite flavor group $G \subset SO(3)$ can have double covering $G^{'} \subset SU(2)$ such that $G \not\subset G^{'}$. This situation is not contradictory, but quite natural, and we give explicit examples such as $G=D_n,…

We introduce the category of C*-discrete inclusions of C*-algebras $A\subset B$ with a faithful conditional expectation $E:B\twoheadrightarrow A$. This class includes many examples such as finite Watatani index inclusions, and also abundant…

We revisit discrete gauge anomalies in chiral fermion theories in $3+1$ dimensions. We focus on the case that the full symmetry group of fermions is $\mathrm{Spin}(4)\times\mathbb{Z}_n$ or…

We study anomalies of non-Abelian discrete symmetries; which part of non-Abelian group is anomaly free and which part can be anomalous. It is found that the anomaly-free elements of the group $G$ generate a normal subgroup $G_0$ of $G$ and…

We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points…

Absract It is proposed that there exist, within a new $SU(2)^{'}$, a gauged discrete group $Q_6$ (the order 12 double dihedral group) acting as a family symmetry. This nonabelian finite group can explain hierarchical features of families,…

We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group $T'$. Otherwise equivalent models based on different $T'$ lead to modular forms with…

The recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two- and three-dimensional irreducible representations. This paper details the mathematics of the two…

Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent…

In the context of discrete flavor symmetries, we elaborate a method that allows one to obtain relations between the mixing parameters in a model-independent way. Under very general conditions, we show that flavor groups of the von Dyck…