Flavor Symmetry and Galois Group of Elliptic Curves

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

2009-03-16

arxiv.org/abs/0903.2718v2

Physics

High Energy Physics

High Energy Physics - Theory

37 pages; the address of one of the authors changed

Scientific paper

A new approach to the generation structure of fermions is proposed. We consider a brane configuration in which the brane intersection yields a two-torus in the extra space. It is assumed that the two-torus is discretized and is given by the torsion points of the elliptic curve over Q . We direct our attention to the arithmetic structure of the elliptic curve with complex multiplication (CM). In our approach the flavor symmetry including the R-parity has its origin in the Galois group of elliptic curves with CM. We study the possible types of the Galois group. The Galois group is shown to be an extension of Z_2 by some abelian group. 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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