  Two-dimensional sigma models are defined for the new manifestly spacetime
supersymmetric description of four-dimensional compactified superstrings. The
resulting target-superspace effective action is constrained by the way the
spacetime dilaton couples to the worldsheet curvature: For the heterotic
superstring, the worldsheet curvature couples to the real part of a chiral
multiplet, and for Type II it couples to the real part of the sum of a vector
multiplet and a tensor hypermultiplet.
  For the Type II superstring, this contradicts the standard folklore that only
a hypermultiplet counts string-loops, explains the peculiar dilaton coupling of
Ramond-Ramond fields, and allows the effective action to be easily written in
N=2 4D superspace. It also implies that vector multiplet interactions get no
quantum corrections, while hypermultiplet interactions can only get corrections
if mirror symmetry is non-perturbatively broken.
