  We study some analytical and geometric properties of a two-dimensional
nonlinear sigma model with gravitino which comes from supersymmetric string
theory. When the action is critical w.r.t. variations of the various fields
including the gravitino, there is a symmetric, traceless and divergence-free
energy-momentum tensor, which gives rise to a holomorphic quadratic
differential. Using it we obtain a Pohozaev type identity and finally we can
establish the energy identities along a weakly convergent sequence of fields
with uniformly bounded energies.
