Spontaneous symmetry breaking (SSB) is a key concept in physics that for decades has played crucial role the description of many physical phenomena large number different areas, like particle physics, cosmology, and condensed-matter physics. SSB thus an ubiquitous connecting several, both "high" "low" energy, areas textbooks describe its basic features great detail. However, to study dynamics l...

We show that solutions for the masses and mixings of the quarks and leptons based on a U (1)×Z 2 horizontal symmetry are possible. The seesaw mechanism is shown to work consistently in the presence of the discrete symmetry. The discrete symmetry results in the phenomenologically useful suppressions of elements of the Yukawa matrices. The quark and lepton masses, the CKM mixing angles, and the n...

Recently it was shown that discrete R-invariance in superpotential can lead to a successful flat potential in inflation. We suggest that this discrete R-symmetry arises from an underlying supersymmetric gauge theory, which gives rise to a scalar inflaton as a composite field. This discrete R-symmetry is common to the dynamical breaking scenarios in global supersymmetry studied several years ago...

In the following, isomorphism of an arbitrary finite group of symmetry, non-crystallographic symmetry (quaternion groups, Pauli matrices groups, and other abstract subgroups), in addition to the permutation group, are considered. Application of finite groups of permutations to the packing space determines space tilings by policubes (polyominoes) and forms a structure. Such an approach establish...

We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so–called perfect actions, with exact symmetries and we will review first steps towards this end.