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 CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of |χ . 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.

Who changes the string coupling?

“…[6]. This work was extended recently to prove the off-shell "ghost-dilaton theorem" in covariant quantum closed string field theory [7,8]. This result states that an infinitesimal shift along the zero-momentum ghost-dilaton changes the quantum string action, or more precisely, the path integral string measure, in a way equivalent to a shift in the dimensionless string coupling.…”

“…Such hamiltonian will take a form similar to that of Ref. [7] and will allow us to treat in a uniform way the dilaton, the ghost-dilaton, the matter-dilaton and the graviton-trace states. We explain what kind of deformations these various states produce, and emphasize that none of them leads to a change of the slope parameter α ′ .…”

“…Note that this hamiltonian may involve a state χ which is not annihilated by b − 0 since this state only appears inserted on three punctured spheres and there is no problem defining the phase of a local coordinate on such collection of surfaces (see [7]). Using this hamiltonian we will be able to treat ghost and matter dilatons in a similar fashion.…”

“…Using this hamiltonian we will be able to treat ghost and matter dilatons in a similar fashion. We now follow [7] to compute the right hand side of (5.6). Since the computation is rather similar, we will be brief.…”

“…[10]. Indeed, following [7] the deformation can be absorbed by a change of basis generated by the ghost-number operator. For integrated correlators this cannot be done, implying that the matter dilaton alters the string coupling.…”