Gaugino Condensation, Loop Corrections, and S-Duality Constraint

Abstract

Amongst the candidates for fundamental unified theories, heterotic superstring theory with gauge group E ₈ × E ₈ seems to be the most promising one. This is because the spectrum of the theory easily accomodates the Standard Model spectrum and gauge structure. In addition, the underlying gauge group contains an extra factor of E ₈ which provides an ‘hidden sector’, which couples to the observable sector only through gravity, and, as will be discussed below, plays a crucial role in the mechanism of supersymmetry breaking. Furthermore, the effective theories that describe the heterotic string in 4 dimensions below the Planck scale are (nonrenormalizable) locally supersymmetric effective field theories. Indeed, requiring supersymmetry at energies well above M _w in order to stabilize the gauge hierarchy, in some sense forces one to consider locally supersymmetric theories: A unified field theory must include gravity. Within the framework of General Relativity, a supersymmetric theory has to be locally supersymmetric. This follows from the fact that the supersymmetry transformation on the metric, or on the vielbein must include general coordinate transformations. Supergravity theories are nonrenormalizable, but can be consistently viewed as low-energy effective field theories (LEEFT) for the massless modes of superstring.