Galois Group of Elliptic Curves and Flavor Symmetry
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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.
37 pages, v2: detailed explanation of the relation between the Galois group and the symmetry of open strings added, the interpretation of D-brane configuration changed, references added
37 pages, v2: detailed explanation of the relation between the Galois group and the symmetry of open strings added, the interpretation of D-brane configuration changed, references added