Construction of Fermionic String Models in Four Dimensions

Abstract

Abstract The construction of four-dimensional closed fermionic string models is discussed. The approach is based on a fermionic formulation of all internal (i.e. toroidally compactified) coordinates. Modular invariance, world sheet supersymmetry, (super)conformal invariance and proper space-time spin-statistics impose stringent constraints on the model building. Using these constraints on the boundary conditions (spin structure) of the world sheet fermions, we obtain a simple set of rules for constructing ultraviolet-finite closed fermionic string models. For a large subclass of these models, this “spin structure” construction can be related to bosonic constructions via the fermionic charge lattice. These charge lattices are odd lorentzian self-dual lattices shifted by a fixed vector and form a nontrivial generalization of the lorentzian self-dual even-integer lattices considered by Narian. In particular, four-dimensional models with N = 4, N = 2, and N = 1 supersymmetry as well as non-supersymmetric tachyon-free chiral models can easily be construted. Some models may be interpreted as charge lattices moded by discrete symmetries - in particular Z2 type orbifolds. String interactions and other related issues are also discussed.