Couplings in asymmetric orbifolds and grand unified string models

Using the bosonic supercurrent (or covariant lattice) formalism, we review how to compute scattering amplitudes in asymmetric orbifold string models. This method is particularly useful for calculating scattering of multiple asymmetrically twisted string states, where the twisted states are rewritten as ordinary momentum states. We show how to reconstruct some of the three-family grand unified string models in this formalism, and identify the quantum numbers of the massless states in their spectra. The discrete symmetries of these models are rather intricate. The superpotentials for the three-family E₆ model and a closely related SO(10) model are discussed in some detail. The forms of the superpotentials of the two three-family SU(6) models (with asymptotically free hidden sectors SU(3) and SU(2) ⊗ SU(2)) are also presented.