Nuclear Physics B315 (1989) 79-120 North-Holland, Amsterdam A REPARAMETRIZATION-INVARIANT APPROACH TO SUPERSTRING FIELD THEORY* Gary KLEPPE, Pierre RAMOND and R. Raju VISWANATHAN Department of Physics, University of Florida, Gainesville, FL 32611, USA Received 7 September 1988 We extend to supersymmetry our program for constructing invariant open string field theories. We discuss the representation theory of reparametrizations and super-reparametrizations, and define covariant derivatives. We then show how to take products of representations and construct invariants. This enables us to list invariants under these transformations. In particular, we find that the BRST charge emerges as the space-time trace of an invariant second-rank tensor. 1. Introduction In an early attempt at devising a covariant field theory of strings [1], classical equations of motion in the free string field theory were proposed. The guiding principle was to identify quantities which transformed covariantly under repar- ametrizations. The requirement of reparametrization invariance yielded a unique set of classical equations of motion, which proved intractable because of their non-lin- earity (there has been a recent attempt at solving these equations [2]). In particular, ordering ambiguities in the operators of the theory were not properly taken into account, giving rise to anomalies in the covariance of the operators, and thus rendering the theory inconsistent. In a recent publication [3], we have revived this formalism. Inspired by the work of Brink and others [4], we added a one-dimensional "einbein" field which cancelled the anomalies, thus restoring the consistency of the theory. The einbein was identified with the Faddeev-Popov ghosts of the theory (unknown to us a similar point of view had been advocated by Tseytlin [5] and Miienster [6]). A unique invariant dynamical (i.e. one containing time derivatives) operator was constructed: the BRST charge [7, 8]. In this paper, we continue the development of this theory to open superstrings. The reparametrization algebra is extended to include its square-root algebra. A general class of representations of this graded algebra is constructed: the doublets. * This work has been supported in part by the U.S. Department of Energy under contract no. DE-FG05-86-ER40272. 0550-3213/89/$03,50©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)