Higher Genus Moduli Spaces in Closed String Field Theory

We provide an overview of covariant closed string field theory, covering briefly the geometry of moduli spaces of Riemann surfaces, conformal field theory in the operator formalism and the Batalin-Vilkovisky formalism. Several important applications are also described including connections on the space of conformal theories, quantum background independence, the ghost-dilaton theorem, and string field theory around non-conformal backgrounds. The proof of the ghost-dilaton theorem in string theory is completed by showing that the coupling constant dependence of the vacuum vertices appearing in the closed string action is given correctly by one-point functions of the ghost-dilaton. To prove this at genus one the formalism required to evaluate off-shell amplitudes on tori is developed. Higher order background independence conditions arising from multiple commutators of background deformations in quantum closed string field theory are analysed. The conditions are shown to amount to a vanishing theorem for As cohomology classes. This holds by virtue of the existence of moduli spaces of higher genus surfaces with two kinds of punctures. Our result is a generalisation of a previous' genus zero analysis relevant to the classical theory. The string theory operators a, CK and I are shown to be expressible as inner derivations of the B-V algebra of string vertices. As a consequence, the recursion relations for the string vertices are found to take the form of a 'geometrical' quantum master equation, {B, B} + AB = 0, where 'B' is the sum of string vertices. That the B-V delta operator cannot be an inner derivation on the algebra is also shown. The set of string vertices of non-negative dimension is completed in a consistent manner. As a consequence the string action takes the simple form S = f(B). That the action satisfies the B-V master equation follows immediately from the recursion relations for the string vertices. The set of string vertices is then extended to include moduli spaces having all integral values of g, n, T > 0. It is argued that the string background, and also the B-V delta operator should be identified with the space B3, 1. This leads naturally to the proposal that the manifest background independent formulation of quantum closed string field theory is given by the sum of the completed set of string vertices B = ,n,o satisfying the classical master equation {B, B} = 0. Thesis Supervisor: Barton Zwiebach Title: Associate Professor