Abstract
In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a ’t Hooft anomaly. In practice, preserving a symmetry that is realized on fermions in a chiral manner necessitates some dynamics beyond simple quadratic mass terms. We show how this can be achieved using familiar results about the strong coupling dynamics of supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4D fermions that carry the quantum numbers of one generation of the standard model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly.
- Received 1 October 2020
- Revised 14 January 2021
- Accepted 12 February 2021
DOI:https://doi.org/10.1103/PhysRevX.11.011063
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
The subatomic particles known as fermions come in two types—left-handed or right-handed—depending on how their spin aligns with their momentum. It is a striking fact that fermions are “chiral,” meaning that the left- and right-handed types experience different forces, and this has important consequences. In particular, it has long been thought that such chiral fermions can get a mass only by coupling to a particle called a Higgs boson. Here, we show that this long-held assumption is incorrect. While we do not suggest that the Higgs boson does not exist, we do show that there is no logical necessity for the fermions to get a mass in this manner.
Specifically, we show that it is possible for chiral fermions to get a mass without the accompanying “electroweak symmetry breaking” that comes with the Higgs boson. If chiral fermions are to get a mass without symmetry breaking, then they must interact strongly with some other quantum fields. The strong interactions mean that it is challenging to understand what is going on. We provide concrete but solvable models, in which we demonstrate that chiral fermions can get a mass with electroweak symmetry unbroken.
These results are important for a number of reasons. In particular, there is optimism that they will help solve the long-standing problem of how to numerically simulate chiral fermions, where unwanted “doubler” fermions must be made massive through a mechanism like the one we discovered.
