Nucleon decay in gauge unified models with intersecting $D$6-branes
Résumé
Baryon number violation is discussed in gauge unified orbifold models of type II string theory with intersecting Dirichlet branes. We consider setups of $D$6-branes which extend along the flat Minkowski space-time directions and wrap around 3-cycles of the internal 6-d manifold. Our study is motivated by the enhancement effect of low energy amplitudes anticipated for M-theory and
type $II$ string theory models with matter modes localized at points of the internal manifold. The conformal field theory formalism is used to evaluate the open string amplitudes at tree level. We study the single baryon number violating processes of dimension 6 and 5, involving four quarks and leptons and in supersymmetry models, two pairs of matter fermions and superpartner sfermions. The higher order processes associated with the baryon number violating operators of dimension 7 and 9 are also examined, but in a qualitative way. We discuss the low energy representation of string theory amplitudes in terms of infinite series of poles associated to exchange of string Regge resonance and compactification modes. The comparison of string amplitudes with the equivalent field theory amplitudes is first studied in the large compactification radius limit. Proceeding next to the finite compactification radius case, we present a numerical study of the ratio of string to field theory amplitudes based on semi-realistic gauge unified non-supersymmetric and supersymmetric models employing the $Z_3$ and $Z_2$ × $Z_2$
orbifolds. We find a moderate enhancement of string amplitudes which becomes manifest in the regime where the gauge symmetry breaking mass parameter exceeds the compactification mass parameter, corresponding to a gauge unification in a seven dimensional space-time
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