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 χ _z¯⁺ is examined in detail for slices supported at two points x₁ and x₂, χ _z¯⁺=ζ ¹δ(z,x ₁)+ζ ²δ(z,x ₂) , 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 x_α, as well as from the superghost insertion points p_a, q_α introduced earlier as computational devices. In particular, the measure is completely unambiguous. The limit x_α= q_α 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.