Two-loop superstrings III: Slice independence and absence of ambiguities Original Research Article

The chiral superstring measure constructed in the earlier papers of this series for general gravitino slices χz̄+ is examined in detail for slices supported at two points x1 and x2, χz̄+=ζ1δ(z,x1)+ζ2δ(z,x2), where ζ1 and ζ2 are the odd Grassmann valued supermoduli. In this case, the invariance of the measure under infinitesimal changes of gravitino slices established previously is strengthened to its most powerful form: the measure is shown, point-by-point on moduli space, to be locally and globally independent from xα, as well as from the superghost insertion points pa, qα introduced earlier as computational devices. In particular, the measure is completely unambiguous. The limit xα=qα is then well defined. It is of special interest, since it elucidates some subtle issues in the construction of the picture-changing operator Y(z) central to the BRST formalism. The formula for the chiral superstring measure in this limit is derived explicitly.