Abstract
We review the conditions for consistent propagation of closed strings in background fields and discuss the connection between conformal invariance and the vanishing of the renormalization-group \ensuremath{\beta} functions for the generalized \ensuremath{\sigma} model on a curved world sheet. The \ensuremath{\beta} functions with up to four derivative terms are found to be compatible with graviton and dilaton equations of motion provided the former are computed in a nonminimal subtraction scheme. Finally, vertex operators in background fields are discussed and it is shown that the anomalous dimension operator is given by the first variation of the \ensuremath{\beta} function to all orders in \ensuremath{\alpha}'.
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