Presence or absence of light moduli: The controlling feature for supersymmetry phenomenology

Supersymmetry and string theory suggest the existence of light moduli. Their presence, or absence, controls the realization of supersymmetry at low energies. If there are no such fields, or if all such fields are fixed in a supersymmetric fashion, the conventional thermal production of lightest supersymmetric particle dark matter is possible, as is an anomaly-mediated ("mini-split") spectrum. On the other hand, the axion solution to the strong CP problem is not operative, and slow roll inflation appears difficult to implement. If there are light moduli, a mini-split spectrum is less generic, weakly interacting dark matter appears atypical, and the supersymmetry scale is likely tens of TeV or higher.