Sewing βγ theories on Riemann surfaces in the global operator formalism

Abstract

We apply the global operator bosonization on Riemann surfaces in order to describe the sewing of the bcβγ (reparametrization/superconformal ghosts) theories. The non-trivial part is the βγ sector, where a complicated rearrangement of the structure of spurious poles is to be accounted for. Yet the bc theory is also included, which allows us to develop a unified treatment for the ghost/superghost system in the phase II bosonization (related to the superfield “super”-bosonization). It turns out that sewing can be accomplished by two kinds of transformations of the global bosonization scheme: (i) a redefinition of the basic bosonic currents, and (ii) a “form-variation” of a composite bosonic operator (the background operator) which represents the minimal set of the bcβγ field operator insertions. The “form-variation” is explicitly implemented by multiplying the background operator with a certain composite bosonized operator. Both (i) and (ii) should be followed by normal re-ordering, since the intrinsic (“global”) normal ordering prescription on a Riemann surface varies with the surface.