Flavor Symmetries and Winding Modes

TL;DR

This paper explores how string theory compactifications give rise to modular flavor symmetries, revealing intricate structures of massive states, dualities, and discrete remnants of gauge symmetries that influence flavor physics and potential collider signatures.

Contribution

It provides a detailed analysis of the emergence of modular flavor symmetries from string dualities, including the role of massive states and the origin of non-Abelian discrete symmetries from continuous gauge symmetries.

Findings

Modular flavor symmetries originate from string dualities via orbifolding.

Massive states form towers with different quantum numbers, becoming massless at various moduli points.

Discrete flavor symmetries are remnants of continuous gauge symmetries, with implications for collider searches.

Abstract

Modular flavor symmetries have been proposed as a new way to address the flavor problem. It is known that they can emerge from string compactifications. We discuss this connection in detail, and show how the congruence subgroups of SL(2,Z), which underlie many modular flavor symmetries, emerge from stringy duality symmetries by orbifolding. This requires an analysis of massive states, which reveals a picture that is more intricate than the well-known situation on the torus. It involves towers of states of different quantum numbers, related by modular transformations. Members of different towers become massless at different points in moduli space. We also show that, at least in the Z_3 orbifold, the string selection rules can be understood as discrete remnants of continuous gauge symmetries. Non-Abelian discrete flavor symmetries arise as relics of various, relatively misaligned, continuous Abelian gauge symmetries. The generators of these U(1) symmetries give rise to CP-violating Clebsch-Gordan coefficients. If the modulus settles close to a critical point, the corresponding gauge bosons may be light enough to be searched for at future colliders.