Galois Group of Elliptic Curves and Flavor Symmetry

Details Galois Group of Elliptic Curves and Flavor Symmetry Galois Group of Elliptic Curves and Flavor Symmetry

2007-10-16

arxiv.org/abs/0710.2959v2

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, v2: detailed explanation of the relation between the Galois group and the symmetry of open strings added, the interp

Scientific paper

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.

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