The dilaton theorem and closed string backgrounds

Abstract

The zero-momentum ghost-dilaton is a non-primary BRST physical state present in every bosonic closed string background. It is given by the action of the BRST operator on another state |χ〉 but remains nontrivial in the semirelative BRST cohomology. When local coordinates arise from metrics we show that dilaton and |χ〉 insertions compute Riemannian curvature and geodesic curvature respectively. A proper definition of a CF T deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of |λ〉 Surprisingly, the ghost number anomaly makes this a trivial deformation. While dilatons cannot deform conformal theories, they actually deform conformal string backgrounds, showing in a simple context that a string background is not necessarily the same as a CFT. We generalize the earlier proof of quantum background independence of string theory to show that a dilaton shift amounts to a shift of the string coupling in the field-dependent part of the quantum string action. Thus the “dilaton theorem”, familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action.