What is the discrete gauge symmetry of the minimal supersymmetric standard model

Proton hexality in local grand unification

“…Before discussing orbifold compactifications of the heterotic string, let us demonstrate how the previous problems are solved in a bottom-up approach with two extra dimensions 6 . For simplicity, we construct the previously described Pati-Salam times U(1) X model in four dimensions.…”

“…5 Note that in the case of matter parity as a subgroup of SO(10) we would need a 126-dimensional representation to get the desired symmetry breakdown. 6 In the spirit of [14] this may correspond to a compactification of the heterotic string on T 6 /Z M × Z N , where our T 2 appears as a fixed torus under the Z N factor. For a list of possible Z M × Z N orbifolds see e.g.…”

“…Anomaly cancellation restricts the spectrum of a gauge theory leading to a finite number of possible discrete symmetries, which can be obtained in such a way. The authors of [6] looked through all such symmetries and identified proton hexality, P 6 , as the only other phenomenologically interesting discrete symmetry. On SM fields P 6 , as defined by the charge assignments in Table 1, acts as a Z 6 symmetry which is the product of baryon triality and matter parity.…”

“…Interactions including right-handed neutrinos do not introduce baryon number violating terms, since their B 3 charge is zero. All terms needed for the see-saw mechanism are allowed by P 6 [6].…”

“…The situation becomes much more dramatic for the remaining fields: (4, 1, 2) 7 , (4, 1, 2) −7 and the fields in eqn. (6). These are embedded in SO (12) representations containing weights of the form (±7/2, .…”