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

Some No-go Theorems for String Duals of Non-relativistic Lifshitz-like Theories