On the dynamics of superstring compactification

Compactification of the ten-dimensional heterotic superstring theory to four dimensions gives rise to two moduli potentials , , the positive semi-definiteness of which places constraints on the Euler characteristic of the internal space and the adiabatic index of the effective matter source of energy-density and pressure that generates the physical four-space , namely , , or , . Here, we show how fermion-bilinear condensation in the internal space, first put forward by HelayA << l-Neto and Smith, determines the field , thus reducing the moduli space to a single canonical field with a potential Ee , which is positive semi-definite under the same conditions that ensure positive semi-definiteness of , , and has a minimum at a value of that is approximately constant far from the Planck era at . The fields , , which are canonically normalized in the zero-slope limit, are modified by contributions originating from the higher-derivative gravitational terms and , but the associated kinetic energy remains positive for times , guaranteeing classical stability of the solution, since the generalized indeterminacy principle implies a minimum physically measurable time for the superstring theory.