  We study possibilities of string theory embeddings of the gravity duals for
non-relativistic Lifshitz-like theories with anisotropic scale invariance. We
search classical solutions in type IIA and eleven-dimensional supergravities
which are expected to be dual to (2+1)-dimensional Lifshitz-like theories.
Under reasonable ansaetze, we prove that such gravity duals in the
supergravities are not possible. We also discuss a possible physical reason
behind this.
