Supersymmetric quantization of linearized supergravity

Abstract

We give a manifestly supersymmetric quantization scheme for linearized supergravity, motivated by the desire to develop a background field method for the full non-linear theory. Supersymmetric gauge-fixing constraints are constructed and the corresponding ghost action is discussed. It is found that the Faddeev-Popov action itself possesses invariances, requiring “secondary” gauge fixing, which in turn leads to “secondary” ghost fields, the latter having normal statistics. The gauge-fixing constraints are used to construct gauge-fixing terms in the action, with a total of four gauge-fixing parameters. The superpropagators are found and may be greatly simplified by certain choices of these parameters.