Exponential Hierarchies from Anderson Localization in Theory Space.

Area of Science:

• Theoretical Physics
• High Energy Physics
• Condensed Matter Physics

Background:

• Exponential hierarchies in fundamental parameters are a key feature of the Standard Model.
• The origin of these hierarchies, such as the smallness of neutrino masses and the ordering of quark masses, remains unexplained.
• Anderson localization describes the confinement of electron wave functions in disordered materials.

Purpose of the Study:

• To introduce a novel mechanism for generating exponential hierarchies in four-dimensional field theories.
• To explore the analogy between Anderson localization and mass localization in a disordered 'theory space'.
• To investigate the potential application of this mechanism to Standard Model parameter hierarchies and the electroweak hierarchy problem.

Main Methods:

• Developed a theoretical framework inspired by Anderson localization in one-dimensional disordered systems.
• Applied the concept of localized mass eigenstates in a 'theory space' with random mass parameters.
• Investigated the localization of fields with arbitrary spin.

Main Results:

• Demonstrated that mass eigenstates can be exponentially localized in theory space, even with weak disorder.
• Showed that localized mass eigenstates lead to exponentially suppressed couplings.
• Applied the mechanism to explain the smallness of neutrino masses and the ordering of quark masses.

Conclusions:

• Disorder provides a viable mechanism for generating the large hierarchies observed in the Standard Model.
• This framework offers a potential explanation for phenomena beyond the Standard Model, including the electroweak hierarchy problem.
• The findings suggest that disorder, rather than fundamental order, may be responsible for some of the universe's most significant mass scales.