On the heterotic string loop expansion Original Research Article

The effective action for the bosonic sector of the heterotic superstring theory, considered as an expansion in string loops, is reduced to four dimensions, with particular regard to the effects of the one-loop, parity-even term involving the eight-form image introduced by Green et al. Formulae are given for the one-loop corrections to the ten-dimensional, tree-level quartic gravitational term image, which determines the renormalization of the four-dimensional quadratic term image via image. We also derive the formula for the four-dimensional, gauge kinetic function up to two loops, image, where image and image are moduli and γ is the unknown two-loop coefficient of the image string. In the theory of gaugino condensation in the hidden sector, based upon the no-scale supergravity theory, the parameter β determines the ratio of the masses of the gaugino and gravitino to one loop, image. The torus approximation for the internal space image predicts, setting image, image, that this ratio is close to unity, image, while the six-sphere would yield a somewhat smaller ratio, image.