Construction of four-dimensional strings.

Abstract

A systematic study of the general properties of four-dimensional heterotic strings is carried out. These are strings constructed from (22;10) self-dual lattices. The constraints from supercurrent, chirality, and spacetime supersymmetry are discussed. Each of them helps to nail down the self-dual lattice constructed by the gluing method. Eleven general theorems are proved in Sec. IV, on the existence or absence of tachyons, adjoint-representation Higgs particles, higher-spin massless objects, and possible gauge groups in the theory. The questions of chirality and shadow matter are also investigated. For example, it is shown that a string containing the standard-model group and one generation of fermions, as well as 16 dimensions of shadow matter, is necessarily nonchiral no matter how many generations of fermions or what kinds of Higgs particles are present. The theorems proved in this paper are for a specific choice of the supercurrent, that which is used in the ${\mathrm{Z}}_{3}$ orbifold, though similar theorems can be proved for other supercurrents.