Non-invertible flavor symmetries in magnetized extra dimensions

TL;DR

This paper explores non-invertible flavor symmetries in magnetized extra dimensions, revealing their role in shaping the flavor structure of chiral zero modes, which could model quark and lepton generations.

Contribution

It derives fusion rules for non-invertible symmetries in magnetized toroidal compactifications and links these symmetries to the flavor structure of zero modes in string-inspired models.

Findings

Non-invertible symmetries act on chiral zero modes.

Fusion rules for discrete isometry operators are established.

Zero modes' wave functions follow specific selection rules.

Abstract

We discuss non-invertible symmetries in toroidal compactifications of higher dimensional Yang-Mills theory with magnetic fluxes, which can be regarded as an effective action of type IIB string theory with magnetized D-branes. Specifically, we derive fusion rules of discrete isometry operators, which are invariant under the $\mathbb{Z}_N$ orbifold twist. It turns out that degenerate chiral zero-modes non-trivially transform under the non-invertible symmetries in the context of quantum mechanics. Hence, non-invertible symmetries correspond to flavor symmetries of chiral zero modes and determine their flavor structure. We explicitly show the representations and selection rules of chiral zero modes on their wave functions. These zero modes may correspond to generations of quarks and leptons in four-dimensional low-energy effective field theory.