Symmetries of symmetries and geometrical CP violation

Abstract

We investigate transformations which are not symmetries of a theory but nevertheless leave invariant the set of all symmetry elements and representations. Generalizing from the example of a three Higgs doublet model with $\Delta (27)$ symmetry, we show that the possibility of such transformations signals physical degeneracies in the parameter space of a theory. We show that stationary points only appear in multiplets which are representations of the group of these so-called equivalence transformations. As a consequence, the stationary points are amongst the solutions of a set of homogeneous linear equations. This is relevant to the minimization of potentials in general and sheds new light on the origin of calculable phases and geometrical CP violation.

arXiv comment20+9 pages, 1 figure; v1: minor changes, added clarification, matches the published version

References in corpus (22)

• Jarlskog-like invariants for theories with scalars and fermions
• Minkowski space structure of the Higgs potential in 2HDM
• CP and Discrete Flavour Symmetries
• CP Violation from Finite Groups
• Automorphisms in Gauge Theories and the Definition of CP and P
• Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
• Symmetry breaking patterns in 3HDM
• A common origin of fermion mixing and geometrical CP violation, and its test through Higgs physics at the LHC
• Geometrical CP violation from non-renormalisable scalar potentials
• Generalized CP symmetries in Delta(27) flavor models
• Geometrical CP Violation
• Discrete symmetries in the three-Higgs-doublet model
• Stability of the normal vacuum in multi-Higgs-doublet models
• Neutrino Mixing and Geometric CP Violation with Delta(27) Symmetry
• Properties of the general NHDM. I. The orbit space
• Geometric minimization of highly symmetric potentials
• Geometrical CP violation in multi-Higgs models
• Geometrical CP violation with a complete fermion sector
• Constraining multi-Higgs flavour models
• Geometrical CP violation in the N-Higgs-doublet model
• Towards realistic models of quark masses with geometrical CP violation
• Flavor Delta(54) in SU(5) SUSY Model

Cited by in corpus (21)

• Pieces of the Flavour Puzzle
• Towards a complete $\Delta (27)\times SO(10)$ SUSY GUT
• Invariant approach to CP in unbroken $\Delta (27)$
• Invariant approach to CP in family symmetry models
• Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector
• CP-odd invariants for multi-Higgs models: applications with discrete symmetry
• Minima of multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• When the C in CP does not matter: anatomy of order-4 CP eigenstates and their Yukawa interactions
• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Multi-Higgs models with CP symmetries of increasingly high order
• Breaking classical Lie groups to finite subgroups - an automated approach
• Complex $S_3$-symmetric 3HDM
• CP and other Symmetries of Symmetries
• 3HDM with $\Delta (27)$ symmetry and its phenomenological consequences
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• CP as a Symmetry of Symmetries
• Adding CP to flavour symmetries
• Telling compositeness at a distance with outer automorphisms and CP
• Symmetries from outer automorphisms and unorthodox group extensions
• CP-odd invariants for multi-Higgs models and applications with discrete symmetry