(27)³ YUKAWA COUPLINGS AND EMBEDDINGS OF DISCRETE GROUPS IN THE $CP^3\times CP^2/Z_3\times Z'_3$ MODEL

Abstract

It is pointed out that, besides the conventional embedding of the [Formula: see text] discrete group in the Schimmrigk model in which [Formula: see text] is embedded nontrivially, there exists an alternate embedding in which Z3 is nontrivially embedded. It is found that, for the Schimmrigk model deformed from the symmetric point by a single (2, 1)-form (z1z2z3), the deformation introduces six more nonvanishing independent (27)3 Yukawa couplings before flux breaking. The alternate embedding introduces many complex Yukawa couplings, even when the modulo is real, giving rise to automatic CP violation.

CPviolation from the standard model to strings

“…Here the new sources of CP violation can generate large contributions to the EDMs even significantly above the current experimental limits. Here one needs special mechanisms to suppress the EDMs such as mass suppression (Kizukuri and Oshimo, 1992;Nath, 1991) or the cancelation mechanism to control the effect of large CP phases on the EDMs. Nath, 1998a,b,c, 2000d).…”

“…One possible origin is string compactification (Bailin et al, 1998a(Bailin et al, ,b, 2000Dent, 2001Dent, , 2002Faraggi and Vives, 2002;Kobayashi and Lim, 1995;Witten, 1985;Wu et al, 1991). One may call this hard CP violation since this type of CP violations can exist even without soft terms.…”

“…An analysis for case (B) was carried out in (Wu et al, 1991). The Yukawa couplings determined in this fashion have unknown normalizations for the kinetic energy.…”

Is the Gepner three generation model phenomenologically viable?

“…Therefore, one may have to go beyond the symmetric point (i.e., the Schimmrigk model with nonzero moduli) to find a phenomenologically more interesting model, as shown in Ref. [13] for a simple case with only one nonvanishing modulus, where an interesting model has been found which demonstrates an automatic CP violation. It is thus of interest to study the model represented in Ref.…”

“…Of two possible flux-breaking patterns [12], we are interested in the one which produces nine lepton, six mirror-lepton, three quark, three antiquark and no mirror-quark or mirror antiquark generations [7,11,13]. These massless fields can be represented by their SU (3),_X SU(3)L X SU (3) (3), X SU(2), X U(1), signaled by the scalar ( m a d 2 turning negative, via the renormalization group equations [14].…”