Two-loop superstrings III - Slice independence and absence of ambiguities

The chiral superstring measure constructed in the earlier papers of this series for general gravitino slices chi((z) over bar)(+) is examined in detail for slices supported at two points chi(1) and chi(2), chi((z) over bar)(+) = zeta*delta(z, chi(1)) + zeta(2)delta(z, chi(2)), where zeta(1) and zeta(2) 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 chi(alpha), as well as from the superghost insertion points p(a), q(alpha), introduced earlier as computational devices. In particular, the measure is completely unambiguous. The limit chi(alpha) = q(alpha) 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. (C) 2002 Elsevier Science B.V. All rights reserved.