Galois Group of Elliptic Curves and Flavor Symmetry

TL;DR

This paper explores how the Galois group of elliptic curves with complex multiplication can serve as the origin of flavor symmetries in particle physics, linking algebraic number theory with string theory and fermion mass structures.

Contribution

It introduces a novel approach connecting Galois groups of elliptic curves with complex multiplication to flavor symmetry generation in particle physics models.

Findings

Identifies possible Galois groups from elliptic curves with CM.

Constructs a phenomenologically viable model matching fermion mass textures.

Ensures mixed-anomaly conditions are satisfied in the proposed framework.

Abstract

Putting emphasis on the relation between rational conformal field theory (RCFT) and algebraic number theory, we consider a brane configuration in which the D-brane intersection is an elliptic curve corresponding to RCFT. A new approach to the generation structure of fermions is proposed in which the flavor symmetry including the R-parity has its origin in the Galois group on elliptic curves with complex multiplication (CM). We study the possible types of the Galois group derived from the torsion points of the elliptic curve with CM. A phenomenologically viable example of the Galois group is presented, in which the characteristic texture of fermion masses and mixings is reproduced and the mixed-anomaly conditions are satisfied.