Which String Vibrations Become Which Generations on the Dwork Quintic
We determine, for the heterotic string on the one-parameter family of quintic threefolds, which vibration modes become which families of charged particles. The hundred and one families are labelled by the characters of a symmetry group of order one hundred and twenty-five. Every Yukawa coupling that this symmetry allows is a power of the modulus, and every other coupling vanishes. The invariant deformation pairs each family with exactly one partner, so that fifty families are massless at the Fermat point and none anywhere else, and at the Fermat point the masses are given in closed form by…
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