Is the droplet theory for the Ising spin glass inconsistent with the replica field theory?

Symmetry arguments are used to derive a set of exact identities between irreducible vertex functions for the replica symmetric field theory of the Ising spin glass in zero magnetic field. Their range of applicability spans from mean-field to short-ranged systems in physical dimensions. The replica symmetric theory is unstable for d > 8, as in the mean-field theory. For 6 < d < 8 and d less than or similar to 6, the resummation of an infinite number of terms is necessary to settle the problem. When d < 8, these Ward-like identities must be used to distinguish an Almeida-Thouless line from the replica symmetric droplet phase.