Conformal Field Theory and String Field Theory.

We investigate some aspects of the covariant and gauge invariant open string field theories proposed by Witten. The use of two-dimensional conformal field theory techniques in simplifying calculations and as a conceptual aid are emphasized. We begin by showing that the moments of the BRST current do not anticommute with each other for both bosonic and fermionic strings. We further show that the BRST current is not BRST invariant unless the total derivative terms are chosen in a unique way. These facts are irrelevant for first-quantized string theory but are important in string field theory. Next, the conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_{n} symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed spacetime diffeomorphism invariance is shown to be free of anomalies. A new class of symmetries, including generalizations of the K_{n} symmetries which are local in spacetime, are presented. The conformal field theory representation of Witten's open superstring field theory is discussed. We argue that the previously suggested cubic action for the superstring is actually dependent on the spacetime background, and suggest a modification which formally removes this dependence. The transformation from the new version of the superstring cubic action to Witten's action for open string states is discussed. A class of linearized solutions to the new field equations are exhibited. These solutions are in one-to-one correspondence with the physical excitations of the open and closed type I superstrings.