Noncritical strings, RG flows and holography

We derive an RG flow equation that is satisfied by the regularized partitio n function for noncritical strings in background fields. The flow refers to change in the position of a "boundary" in the Liouville direction. The bou ndary is required to regularize the ultraviolet divergences in the partitio n function coming from integration over world-sheets of arbitrarily small a rea From the point of view of the target space effective gravitational acti on that the partition function evaluates on-shell, the boundary regularizes infrared divergences coming from the infinite volume of the Liouville dire ction. The RG flow equation that we obtain looks very much like the Hamilto n-Jacobi constraint equation that an on-shell gauge-fixed gravitational act ion must satisfy. (C) 2000 Elsevier Science B.V. All rights reserved.