Abstract:
We investigate Weyl anomalies on a curved world sheet to second order in a weak field expansion. Using a local version of the exact renormalization group equations, we obtain nonperturbative results for the tachyon/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 world sheet
allows us to obtain the nonperturbative contributions to the dilaton $\beta$ function. We find the $\beta$ functions, after suitable field redefinitions, to be related to a target space effective action through a $\kappa$ function involving derivatives. Also we can establish a nonperturbative Curci–Paffuti relation including the tachyon $\beta$ function.
Citation:
J. Schnittger, U. Ellwanger, “Nonperturbative conditions for local Weyl invariance on a curved world sheet”, TMF, 95:2 (1993), 361–384; Theoret. and Math. Phys., 95:2 (1993), 643–662