WEYL ANOMALY AND CURCI-PAFFUTI THEOREM FOR SIGMA-MODELS ON MANIFOLDS WITH BOUNDARY

We generalize the relation of the Weyl-anomaly coefficients to renormalization-group functions, and the Curci-Paffuti relation to the case of two-dimensional sigma-models on manifolds with boundary. The analysis is based on the use of minimal subtraction in a regularization with a dimensional cutoff. The renormalization-group functions are different on and off the boundary. This explicit dependence on the position in two-dimensional space raises serious problems for a straighforward string interpretation of the model if fields corresponding to excitations of both open and closed strings are involved.