On Vertex Operators in Effective String Theory

In this note we construct vertex operators in effective string theory using the simplified covariant formalism, i.e. by embedding it in the Polyakov formalism supplemented by an anomaly term, and fixing to conformal gauge. These vertex operators represent off-shell background fields rather than dynamical string states. We construct vertex operators for nontrivial scalar, electromagnetic, and gravitational backgrounds. As an application, we compute a scalar form factor of a long string with length $R$, where the Fourier momentum $q$ of the external scalar field satisfies $q^2 \ll 1/\alpha^\prime$, and we find the expected logarithmic dependence on the size of the string.