Path integrals for the Green-Schwarz superstring

The goal of this dissertation is to develop path integral techniques for the evaluation of amplitudes for the Green-Schwarz superstring. The Green-Schwarz Lagrangian provides a manifestly supersymmetric alternative to the more widely used Neveu-Schwarz-Ramond Lagrangian. Until now, however, path integrals for the Green-Schwarz model have rarely been considered, primarily because of difficulties in gauge-fixing the local fermionic symmetry of the action. It is shown that these difficulties can be overcome for the heterotic string. As a consequence, the standard light cone gauge condition may be applied to the fermions, without necessarily imposing (singular) light cone gauge on the bosons. The resulting theory has no conformal or local Lorentz anomalies. The formalism is applied to the calculation of a number of amplitudes. Although fermionic light cone gauge is not Lorentz invariant, the three level propagator is shown to be invariant up to physically irrelevant phases, and to have the correct pole structure. A number of loop amplitudes are then calculated. It is demonstrated that as long as supersymmetry is unbroken, the vacuum energy vanishes to all orders in perturbation theory, and one- and two-particle S-matrix elements for massless particles receive no higher loop corrections. The one loop amplitude at finite temperature is also investigated; it gives the correct sum of free energies of string modes