Abstract
We elucidate the fate of classical symmetries which suffer from Abelian Adler-Bell-Jackiw anomalies. Instead of being completely destroyed, these symmetries survive as noninvertible topological global symmetry defects with world volume anyon degrees of freedom that couple to the bulk through a magnetic 1-form global symmetry as in the fractional Hall effect. These noninvertible chiral symmetries imply selection rules on correlation functions and arise in familiar models of massless quantum electrodynamics and models of axions (as well as their non-Abelian generalizations). When the associated bulk magnetic 1-form symmetry is broken by the propagation of dynamical magnetic monopoles, the selection rules of the noninvertible chiral symmetry defects are violated nonperturbatively. This leads to technically natural exponential hierarchies in axion potentials and fermion masses.
- Received 3 August 2022
- Accepted 2 February 2023
DOI:https://doi.org/10.1103/PhysRevX.13.011034
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Symmetry principles anchor our understanding of quantum physics and the laws of nature. The idea of symmetry formalizes the intuitive notion of patterns and describes features of particles or spacetime that are invariant under transformations such as translations or rotations. Symmetries offer a unique window into the dynamics of interacting systems of microscopic constituents and organize macroscopic behavior into universality classes based on patterns of symmetry realization. In this work, we define a new class of symmetries and exhibit them in models of massless quantum electrodynamics and axions.
Our focus is on chiral symmetries, whose action is not invariant under reflections in space. These symmetries are ubiquitous, arising in chiral atoms and molecules. In particle physics, chiral symmetries play a key role in gauge theories such as the standard model of particle physics and theories of hypothetical elementary particles known as axions. Often such symmetries are in tension with the laws of quantum mechanics: While they exist classically, their nature is fundamentally altered by quantum anomalies. We show that the resolution of this tension is that the charges defining these symmetries support anyons, particles with fractional spin and charge.
Symmetry can also be useful when it is broken by small effects. Then, the consequences of the symmetry are weakly violated but protected from large corrections. Applying these ideas to our construction, we exhibit an interplay between the physics of magnetic monopoles and exponentially small masses or energy splittings that arise as the leading effects violating our novel chiral symmetries. This provides a symmetry-based mechanism for generating hierarchies, i.e., large ratios of physical quantities.
These ideas might find applications in theories of physics beyond the standard model that seek to explain hierarchies in the masses and couplings of elementary particles.
