A super-worldsheet approach to the heterotic string

This thesis contains three main topics. First a superspace formalism of (1,0) supergravity in 2 dimensions is presented. (1,0) supergravity is the worldsheet symmetry of the heterotic string and the action as well as the Virasoro constraints are given in a superfield form. The worldsheet symmetries and the sigma-model symmetries of the action are discussed in detail. In the second part the manifestly supersymmetric formulation is used to calculate superdiffeomorphic, Lorentz and super-Weyl anomalies. The Wess-Zumino consistency condition is formulated in (1,0) superspace and its solution is given. The superspace relation between the superdiffeomorphic and the Lorentz anomaly is discussed in detail. Using similar methods one can also obtain the sigma-model anomalies of the heterotic string. Their relevance to target space physics is emphasized. The use of a superspace formalism resolves the problems of the component approach. In the third part a method, the S-matrix approach, for deriving a low energy effective Lagrangian in 4 dimensions is presented. As an example the Kaehler potential and the superpotential for the scalar fields of toroidal and orbifold compactifications of the heterotic string are given. The effective Lagrangian is derived without going through a field theory limit of the heterotic string, this is the novel feature of the method presented. It includes the exact string tree level result. The moduli space of these compactifications is discussed in detail. It arises from two different viewpoints, from the low energy Lagrangian and from geometrical considerations