Higgs versus matter in the heterotic landscape

In supersymmetric extensions of the standard model there is no basic difference between Higgs and matter fields, which leads to the well-known problem of potentially large baryon and lepton number violating interactions. Although these unwanted couplings can be forbidden by continuous or discrete global symmetries, a theoretical guiding principle for their choice is missing. We examine this problem for a class of vacua of the heterotic string compactified on an orbifold. As expected, in general there is no difference between Higgs and matter. However, certain vacua happen to possess unbroken matter parity and discrete R-symmetries which single out Higgs fields in the low energy effective field theory. We present a method how to identify maximal vacua in which the perturbative contribution to the μ-term and the expectation value of the superpotential vanish. Two vacua are studied in detail, one with two pairs of Higgs doublets and one with partial gauge-Higgs unification.