The eclectic flavor symmetries of $\mathbb{T}^2/\mathbb{Z}_K$ orbifolds

TL;DR

This paper analyzes the flavor symmetries arising from the four admissible $ ext{T}^2/ ext{Z}_K$ orbifold building blocks in heterotic string compactifications, identifying their representations and implications for model building.

Contribution

It systematically determines the traditional and modular flavor symmetries, including non-Abelian and discrete R-symmetries, for all four orbifold building blocks.

Findings

Identified finite flavor symmetries including $(S_3 imes S_3) times ext{Z}_4$, $T'$, $2D_3$, and $S_3 imes T'$.

Mapped the representations and fractional modular weights of massless matter states.

Provided constraints for consistent ultraviolet model building.

Abstract

Only four $\mathbb{T}^2/\mathbb{Z}_K$ orbifold building blocks are admissible in heterotic string compactifications. We investigate the flavor properties of all of these building blocks. In each case, we identify the traditional and modular flavor symmetries, and determine the corresponding representations and (fractional) modular weights of the available massless matter states. The resulting finite flavor symmetries include Abelian and non-Abelian traditional symmetries, discrete $R$ symmetries, as well as the double-covered finite modular groups $(S_3\times S_3)\rtimes\mathbb{Z}_4$, $T'$, $2D_3$ and $S_3\times T'$. Our findings provide restrictions for bottom-up model building with consistent ultraviolet embeddings.