Higher-level Kac-Moody string models and their phenomenological implications

We present a systematic approach to string compactifications in which some of the gauge interactions are realized at higher Kac-Moody level. This can be realized in the current constructions of four-dimensional strings including symmetric and asymmetric compactifications. It is shown that there exist higher-level models which can be obtained from exactly marginal deformations of a level-one model, and a simple field theory interpretation is provided in terms of flat scalar field directions in the original level-one model. We then consider the phenomenological possibilities opened to four-dimensional higher-level string models. In particular we show how the levels associated to standard model interactions as well as the massless content of the theory are constrained by unitarity and the renormalization group equations. We also consider the prospects for string GUT models. Mechanisms like "missing partner" in SU(5) or "see-saw" neutrino in SO(10) are only possible for k ≥ 5. For E₆ at any level only adjoints or fundamentals can be light. A generic feature of the unification models seem to be the existence of relatively light chiral multiplets transforming like (8, 1, 0) + (1, 3, 0) + (1, 1, 0) under SU(3) × SU(2) × U(1). The problems of neutrino masses and proton stability are reconsidered and a possible simultaneous solution involving a discrete gauge symmetry is suggested.