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Global consistency of string compactifications places constraints on thechiral matter spectrum of a gauge theory which include those necessary for theabsence of cubic nonabelian anomalies, but also contain some additionalconditions. In the class of theories we study, some of these are present in afield theory augmented by anomalous U(1)'s and Chern-Simons terms, but some aregenuinely not present in field theory. Their violation has phenomenologicalimplications, rendering inconsistent many quiver gauge theories with the chiralmatter spectrum of the MSSM. The inconsistent MSSM quivers often violate theconstraints in a particular way that is suggestive of what matter must be addedfor consistency. The preferred matter additions are MSSM singlets withanomalous U(1) charge, hyperchargeless SU(2) triplets, quasichiral Higgs orlepton isodoublet pairs, quasichiral quark isosinglet pairs, and nonabeliansinglets with charge +-1. Smaller numbers of quark isodoublet pairs, leptonpairs with charges (+- 1,+- 2), and chiral fourth families are also found. Wepresent the results of systematic analyses including multiplicity counts ofmatter beyond the standard model and also study the possibility of using thesinglets for a dynamical perturbative \mu-term or for neutrino mass. We alsosystematically study the appearance of additional non-anomalous U(1)'symmetries in the low energy theory and find that family non-universality isvery common. These new physics effects may be observable at the LHC even for alarge string scale close to the Planck scale.

Implications of String Constraints for Exotic Matter and Z' s Beyond the Standard Model