Neutrino Masses from Generalized Symmetry Breaking

TL;DR

The work investigates generalized global symmetries, with a focus on non-invertible chiral symmetries, and shows that their quantum breaking by lepton-family monopoles can naturally yield exponentially small neutrino masses without extensive new fields. By gauging leptonic family differences such as $U(1)_{L_\mu- L_\tau}$ and embedding them into non-Abelian horizontals, the authors derive UV completions where either Majorana or Dirac neutrino masses arise from instanton-like effects, encoded as 't Hooft vertices, and they connect these UV mechanisms to low-energy leptophilic $Z'$ phenomenology. The paper provides a detailed anomaly and RG analysis that delineates the fate of global symmetries after gauging, and offers concrete predictions for the UV scale $v_\Phi$ and the $Z'$ parameters that could be tested at colliders or precision experiments. Overall, the framework links fundamental symmetry structure to a predictive, UV-complete explanation for the smallness of neutrino masses, while identifying experimental signatures of the UV dynamics in leptophilic gauge sectors.

Abstract

We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of $Z'$ bosons generically contain 'non-invertible' chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated $U(1)_{L_μ- L_τ}$, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. $U(1)_{L_μ- L_τ} \subset SU(3)_H$, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. $y_ν\sim y_τ\exp(-S_{\rm inst})$. These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family $Z'$ at low energies will reveal the scale at which $L_μ- L_τ$ emerges from a larger gauge symmetry.

Figures (9)

• Figure 1: An intuitive illustration of Majorana neutrino masses generated by monopole/dyon loops in our models. From an ultraviolet perspective the sum over monopole loops is identified with an instanton process.
• Figure 2: The charge operator $Q[\Sigma]$ wraps a local operator $\mathcal{O}(x)$ in spacetime. Using the topological property, $Q[\Sigma]$ can be shrunk and results in a factor of the charge $q$ of $\mathcal{O}(x)$.
• Figure 3: The action of magnetic one-form symmetry operator $U_\varphi^M$ on a 't Hooft line $T$ (the worldline of a heavy probe monopole). The symmetry operator is spatially placed so that it wraps the heavy monopole in a time slice. Since $U_\varphi^M$ is topological, it can be shrunk towards the monopole worldline, giving the phase $e^\mathrm{i\varphi}$. This is the magnetic version of Gauss' law and generalizes the action in Figure \ref{['fig:zeroform']}.
• Figure 4: When the non-invertible symmetry defect $\mathcal{D}_{kN}$ for the chiral symmetry wraps a loop of 't Hooft line, it induces a fractional $\frac{1}{kN}$ electric charge on the 't Hooft line. Such a dyon with fractional charge has to be attached to the electromagnetic dual of a Dirac string whose world volume is identified with $U_{2\pi /kN}^M$. This indicates that dynamical monopoles break the chiral symmetry.
• Figure 5: A triangle diagram which breaks current conservation of the classical symmetries of the Standard Model.