Bosonized superconformal ghosts and operator construction of g-loop amplitudes

Abstract

Using the operator approach with bosonized representation of the superconformal ghosts β and γ, the g-loop operator is constructed out of vertices and propagators together with a projector. This projector is introduced to restrict the degrees of freedom of the bosonized representation to those of the original βγ system, by specifying the picture of each loop and projecting out redundant zero-modes. Using the g-loop operator, we derive the general correlation functions which can also include spin operators. It is shown that the correlation functions are independent of the picture chosen by the projector. The role of the zero-modes of the fermion fields η and ξ in relation with the Riemann-Roch theorem is clarified. The Feynman-like rules of the superstring are also discussed.