Abstract
Abstract We study the presence of discrete gauge symmetries in D-brane semi-realistic compactifications. After establishing the constraints on the transformation behaviour of the chiral matter for the presence of a discrete gauge symmetry we perform a systematic search for discrete gauge symmetries within local semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM and the MSSM with three right-handed neutrinos. The systematic search reveals that Proton hexality, a discrete symmetry which ensures the absence of R-parity violating terms as well as the absence of dangerous dimension 5 proton decay operators, is only rarely realized. Moreover, none of the semi-realistic local D-brane configurations exhibit any family dependent discrete gauge symmetry.
Highlights
We study the presence of discrete gauge symmetries in D-brane compactifications
We translate the conditions for the presence of a discrete gauge symmetry in D-brane compactifications laid out in [6] into constraints on the transformation behaviour of the chiral matter fields
This allows for a bottom-up search, a search that does not require the knowledge of any features of the compactification manifold, for local D-brane configurations with respect to discrete gauge symmetries
Summary
We investigate all four stack realizations that give rise to the exact MSSM spectrum, satisfy the severe top-down constraints discussed above and pass the phenomenological constraints displayed in appendix A. Such an abelian gauge symmetry and any discrete subgroup of it should be absent, since otherwise the desired Yukawa couplings QLHuUR, QLHdDR and LHdER would be forbidden Apart from this additional U add(1) we find no vector (ka, kb, kc, kd) that satisfies the discrete anomaly constraints (3.14) and (3.16). In contrast to the solution # 1 of table 9 the Proton hexality in solution # 1 and # 12 may be realized as a subgroup of a larger symmetry, namely a combination of the abelian gauge symmetry U add(1) and the discrete symmetry, matter parity R2. In that case one needs a dynamical mechanism to further break the larger symmetry to Proton hexality in order to allow for a μ-term and a Weinberg operator Beyond those discrete gauge symmetries the local D-brane configuration does not exhibit any additional discrete gauge symmetry. In particular the D-brane setup does not possess any family dependent discrete gauge symmetries
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