Strings in background fields:βfunctions and vertex operators

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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 β functions for the generalized σ model on a curved world sheet. The β 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 β function to all orders in α’.