Strings in background fields:βfunctions and vertex operators

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’.