Selection rules in low energy string effective lagrangians

Abstract

Selection rules which restrict elementary particle interactions are derived as the low-energy limit of superstring theory. A general mechanism is demonstrated, in four-dimensional string tree-amplitudes, whereby the supersymmetric trilinear Yukawa-like couplings in the effective lagrangian which violate lepton number vanish, terms which otherwise occur naturally in supersymmetric versions of the standard model. Explicit expressions for the vertex operators, and all cubic bosonic couplings involving the Yang-Mills gauge bosons and the graviton, together with the scalar and anti-symmetric tensor components of gravity are given. There are no √2 α' corrections to the three-point string tree-amplitudes, a result which eliminates any higher derivative trilinear couplings among these fields in the effective action. In this four-dimensional string theory, expressions are derived for the gravitational coupling constant κ and the Yang-Mills coupling constant g YM in terms of the two string parameters: the universal Regge slope parameter which is the origin of the length scale √2 α', and the dimensionless string coupling constant g. We find κ = 1 2 g√2α' and g YM = g .