NONPERTURBATIVE CONDITIONS FOR LOCAL WEYL INVARIANCE ON A CURVED WORLD-SHEET

We investigate Weyl anomalies on a curved world sheet to second order in a weak field expansion. Using a local version of the exact renormal ization group equations, we obtain nonperturbative results for the tac hyon/graviton/dilaton system. We discuss the elimination of redundant operators, which play a crucial role for the emergence of target space covariance. Performing the operator product expansion on a curved wor ld sheet allows us to obtain the nonperturbative contributions to the dilaton beta function. We find the beta functions, after suitable fiel d redefinitions, to be related to a target space effective action thou gh a kappa function involving derivatives. Also we can establish a non perturbative Curci-Paffuti relation including the tachyon beta functio n.