Gauge fixing in string field theory using the Polyakov path integral

Abstract

The gauge-fixed off-shell propagator for free closed string field theory is calculated using the Polyakov path integral for a cylinder with boundary conditions that break reparametrization invariance - the result for open strings is given without proof. This explicitly establishes the connection between gauge transformations in free string field theory and world-sheet diffeomorphisms on the boundaries, giving an attractive geometrical picture for the origin of gauge invariance. A decomposition of the two-dimensional metric is used which does not distinguish between changes in the metric g ab which effectively move the boundary, such as Teichmüller variations, and diffeomorphisms M → M which do not move the boundary. This decomposition requires an overcomplete set of parameters which specify coordinate transformations on the boundary. The choice of ghost sources attached to the propagator is determined by the choice of a minimal set of these parameters from the overcomplete set. The parameters representing coordinate transformations of the boundaries can be included as dynamical fields in two dimensions and as new coordinates for string field theory. Zero modes of these new coordinates are modular parameters for the torus when the ends of the cylinder are brought together. The relationship between these new coordinates and those introduced by other groups is discussed.