Worldsheet Green function
= Worldsheet Green function
A worldsheet Green function inverts the scalar kinetic operator after its zero modes have been removed. In a locally flat complex coordinate it satisfies $-(\pi\alpha')^{-1}\partial\bar\partial G(z,w)=\delta^{(2)}(z-w)$ and is $G(z,w)=-(\alpha'/2)\log|z-w|^2$ up to harmonic and constant terms.