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

TL;DR

This paper proves that classical supergravity solutions dual to (2+1)-dimensional non-relativistic Lifshitz-like theories cannot exist under certain assumptions, highlighting fundamental limitations in string theory embeddings of these models.

Contribution

The authors establish no-go theorems showing the non-existence of certain Lifshitz-like gravity duals in type IIA and eleven-dimensional supergravity.

Findings

No classical supergravity solutions for Lifshitz duals under reasonable assumptions

Discussion of potential physical reasons for these no-go results

Implications for string theory models of non-relativistic holography

Abstract

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.