Operator approach to bosonic string: Multiloop calculation and b-ghost insertion.

Abstract

We construct the /ital g/-loop /ital N/-string vertex using the Feynman-likerules in the operator formalism with bosonized /ital bc/ ghosts. The measurefactor is analyzed in detail, which consists of the ghost /ital g/ vacuum andthe contour integration associated with the /ital b/-ghost insertion. Thegeneral form of the /ital g/ vacuum is derived using the handle operators. Thehandle operator is formulated by the geometrical quantities: period matrix,first Abelian integral, prime form, 1/2 differential, andRiemann constant. Explicit results are given up to two-loop level. The contourintegrations associated with the ghost insertions can be performed explicitlyin the one-loop case, in which we reproduce the well-known formula of theone-loop /ital N/-tachyon amplitude.