Strings in Curved Space and Background Field Equations

Abstract

We consider the propagation of closed bosonic strings in the presence of background fields (graviton and dilaton). The background field equations can be obtained from the requirement that the quantum string theory maintains the Weyl invariance on the world sheet which is a remarkable property of the string theory. Same results can be also derived from the nilpotency condition for the BRST transformation of gauge fixed string action. In addition, it can be shown that the equations have a cosmological constant term from the effect of the string interaction.