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.
- Publication:
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Nuclear Physics B
- Pub Date:
- May 1995
- DOI:
- 10.1016/0550-3213(95)00022-K
- arXiv:
- arXiv:hep-th/9411047
- Bibcode:
- 1995NuPhB.441...76B
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 51 pages, plain tex with phyzzx, two uuencoded figures