The Dilaton Theorem and Closed String Backgrounds

TL;DR

This paper explores the role of the ghost-dilaton in bosonic closed string backgrounds, revealing how dilaton deformations affect string backgrounds and establishing the dilaton theorem's off-shell validity as a symmetry of the string action.

Contribution

It demonstrates that the dilaton induces background deformations without altering conformal invariance, extending the dilaton theorem off-shell as a symmetry of the string action.

Findings

Dilaton deformations compute Riemannian and geodesic curvature.

Dilaton shifts correspond to changes in string coupling.

The dilaton theorem holds off-shell as a symmetry of the string action.

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 $\x$, but remains nontrivial in the semirelative BRST cohomology. When local coordinates arise from metrics we show that dilaton and $\x$ insertions compute Riemannian curvature and geodesic curvature respectively. A proper definition of a CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of $\x$. 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.