Demystifying stringy miracles with eclectic flavor symmetries

TL;DR

The paper tackles a long-standing string-theory selection rule, Rule 4, that evaded explanation by conventional symmetries. It develops an eclectic flavor framework that fuses modular and traditional flavor symmetries, showing how their interplay—via a hybrid $Z_2^{\rm hybrid}$ and a $Z_3^{\rm rot}$-induced non-Abelian $R$-symmetry $S_3^R$—explains Rule 4 in the $\mathbb{Z}_3$ orbifold. It extends the reasoning to higher-order couplings using modular forms of weight and group-theory representations, and discusses how Wilson lines can modify or break the relevant symmetries. The results provide a structured, symmetry-based understanding of string-derived couplings and suggest broader implications for selection rules in effective theories from string compactifications.

Abstract

Effective field theories arising from string compactifications are subject to constraints originating from the duality transformations of string theory. Interpreting these so-called selection rules in terms of conventional symmetries has remained challenging. We show that particular selection rules in heterotic orbifolds can be explained from a subtle interplay between modular and traditional flavor symmetries within the eclectic flavor framework.

Figures (1)

• Figure 3.1: The $\mathds{T}^2/\mathbbm{Z}_{3}$ orbifold and two of its symmetries in the absence of Wilson lines.