CP and other Symmetries of Symmetries

Abstract

Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this thesis pioneers the study of outer automorphisms which are not related to C, P, or T. It is shown how outer automorphisms, in general, relate symmetry invariants and, in theories with spontaneous symmetry breaking, imply relations between different vacuum expectation values. Thereby, outer automorphisms can give rise to emergent symmetries. An example model with a discrete symmetry and three copies of the Standard Model Higgs field is discussed, in which the rich outer automorphism structure completely fixes the Higgs VEVs in their field space direction, including CP violating relative phases. This underlies the phenomenon of spontaneous geometrical CP violation. The possible relevance of outer automorphisms for a wide field of future studies is highlighted.

PhD thesis, 130 pages, http://mediatum.ub.tum.de?id=1307248

References in corpus (24)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• The global electroweak fit at NNLO and prospects for the LHC and ILC
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Stringy origin of non-Abelian discrete flavor symmetries
• Current status of the Standard Model CKM fit and constraints on $\Delta F=2$ New Physics
• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Observation of Time Reversal Violation in the B0 Meson System
• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Basis-independent methods for the two-Higgs-doublet model II. The significance of tan(beta)
• CP Violation in the General Two-Higgs-Doublet Model: a Geometric View
• Symmetry breaking patterns in 3HDM
• Discrete symmetries and model-independent patterns of lepton mixing
• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Discrete symmetries in the three-Higgs-doublet model
• Stability of the normal vacuum in multi-Higgs-doublet models
• Properties of the general NHDM. I. The orbit space
• The Electroweak Vacuum Angle
• Symmetries of symmetries and geometrical CP violation
• Geometrical CP violation in the N-Higgs-doublet model
• A stable Algebraic Spin Liquid in a Hubbard model
• Breaking classical Lie groups to finite subgroups - an automated approach

Cited by in corpus (2)

• Unification of Flavor, CP, and Modular Symmetries
• Transition of Large $R$-Charge Operators on a Conformal Manifold