Abstract
Compactification of the ten-dimensional heterotic E 8 × E 8 superstring theory on the Calabi-Yau manifold due to Tian and Yau yields three chiral families of quarks and leptons. The first realization of the Tian-Yau manifold leads to a large number of physically distinct models with the four-dimensional gauge group, after flux breaking of E 6, being either SU(3) c × SU(3) L × SU(3) R or SU(6) × U(1). An important challenge faced by these models is that of rapid proton decay which can be prevented if suitable matter parities are present. We search for all possible Z n matter parities in these models and find that there is one Z 2 and four distinct Z 3 matter parity candidates. All of them turn out to be non-R-symmetries. We enumerate the models that admit Z 2 and/or Z 3 matter parities.
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