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We analyze the possibilities for new modular invariant ten-dimensional string theories without spacetime supersymmetry which are twisted versions of the closed superstring or of the heterotic string. The most interesting possibility is a tachyon-free theory with gauge group 0(16) ⊗ 0(16), chiral fermions, and a positive one-loop contribution to the cosmological constant.

A prescription for the calculation of any correlation function in orbifold conformal field theory is given. The method is applied to the scattering of four twisted string states, which allows the extraction of operator product coefficients of conformal twist fields. We derive Yukawa couplings in the effective field theory for fermionic strings on orbifolds.

String propagation on the quotient of a flat torus by a discrete group is considered. We obtain an exactly soluble and more or less realistic method of string compactification.