K3 FIBRATIONS AND SOFTLY BROKEN N=4 SUPERSYMMETRIC GAUGE-THEORIES

Global geometry of K3 fibration Calabi-Yau threefolds, with Hedge numb er h(2,1) = r + 1, is used to define N = 4 softly broken SU(r + 1) gau ge theories, with the bare coupling constant given by the dual heterot ic dilaton, and the mass of the adjoint hypermultiplet given by the he terotic string tension. The U(r + 1) Donagi-Witten integrable model is also derived from the K3 fibration structure, with the extra U(1) ass ociated to the heterotic dilaton. The case of the SU(2) gauge group is analyzed in detail. String physics beyond the heterotic point particl e limit is partially described by the N = 4 softly broken theory. (C) 1997 Published by Elsevier Science B.V.