$K3$-Fibrations and Softly Broken $N=4$ Supersymmetric Gauge Theories

Details $K3$-Fibrations and Softly Broken $N=4$ Supersymmetric Gauge Theories $K3$-Fibrations and Softly Broken $N=4$ Supersymmetric Gauge Theories

1996-08-15

arxiv.org/abs/hep-th/9608104v2

Nucl.Phys. B501 (1997) 109-133

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, Latex, no figures. Misprints corrected

Scientific paper

10.1016/S0550-3213(97)00336-2

Global geometry of $K3$-fibration Calabi-Yau threefolds, with Hodge number $h_{2,1}=r+1$, is used to define $N=4$ softly broken $SU(r+1)$ gauge theories, with the bare coupling constant given by the dual heterotic dilaton, and the mass of the adjoint hypermultiplet given by the heterotic string tension. The $U(r+1)$ Donagi-Witten integrable model is also derived from the $K3$-fibration structure, with the extra $U(1)$ associated to the heterotic dilaton. The case of $SU(2)$ gauge group is analyzed in detail. String physics beyond the heterotic point particle limit is partially described by the $N=4$ softly broken theory.

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