We establish conditions under which the worldsheet beta-functions of
logarithmic conformal field theories can be derived as the gradient of some
scalar function on the moduli space of running coupling constants. We derive a
renormalization group invariant version of this function and relate it to the
usual Zamolodchikov C-function expressed in terms of correlation functions of
the worldsheet energy-momentum tensor. The results are applied to the example
of D-brane recoil in string theory.Comment: 12 pages LaTeX; references updated, one added; to be published in
Physics Letters
