Non-supersymmetric four-dimensional strings

Abstract

The general formalism of non-supersymmetric four-dimensional strings is worked out in the Green-Schwarz formalism. The conditions on twisting parameters from world-sheet supersymmetry and Lorentz invariance in the light-cone gauge are shown to be identical. Tachyonic states can be projected out in many models by the modular invariance conditions. Tachyon-free models based on twisting parameters with Z 2, Z 3, Z 4 and Z 6 discrete symmetries are discussed. In particular, the four-dimensional analogue of the tachyon-free ten-dimensional O(16) × O(16) model is obtained. Two specific models with Z 4 and Z 6 symmetry are presented. The Z 6 model has E 6 × U(1) 2 as gauge group, 18 generations of chiral fermions and 17 multiplets of complex scalars in the 27 of E 6 . The Z 4 model has a gauge group SO(10) × SU(2) × U(1) 4, the matter in 4 · ( 16) + 2 · ( 16 + 16) of SO(10) chiral fermions and complex scalars, and a Higgs scalar in the adjoint representation of the gauge group.