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

Wei Li, Tatsuma Nishioka, Tadashi Takayanagi

TL;DR

The paper analyzes whether gravity duals to non-relativistic Lifshitz-like theories can be embedded in string/M-theory via classical supergravity. Through detailed flux-Ansatz no-go arguments, it shows Li4×M7 in M-theory and Li4×M6 in massive IIA are not realizable under plausible Ansätze, even with warp factors or orientifolds. The results suggest intrinsic obstructions to Lifshitz holography within conventional ten- and eleven-dimensional supergravity, and motivate exploring non-standard frameworks or alternative duals. A physical interpretation ties Lifshitz realizations to noncommutative structures, offering insight into why these embeddings are challenging.

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.

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

TL;DR

The paper analyzes whether gravity duals to non-relativistic Lifshitz-like theories can be embedded in string/M-theory via classical supergravity. Through detailed flux-Ansatz no-go arguments, it shows Li4×M7 in M-theory and Li4×M6 in massive IIA are not realizable under plausible Ansätze, even with warp factors or orientifolds. The results suggest intrinsic obstructions to Lifshitz holography within conventional ten- and eleven-dimensional supergravity, and motivate exploring non-standard frameworks or alternative duals. A physical interpretation ties Lifshitz realizations to noncommutative structures, offering insight into why these embeddings are challenging.

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.

Paper Structure

This paper contains 14 sections, 59 equations.

Table of Contents

  1. Introduction
  2. Review of Gravity Duals of Lifshitz-like Fixed Points
  3. No-Go Theorem for $Li_4\times M_7$ in M-theory
  4. Direct Product Metric $Li_4\times M_7$
  5. Warp Factor in $Li_4\times M_7$
  6. Massive IIA Supergravity on $Li_4\times M_6$
  7. Massive IIA theory
  8. No-go Argument in Massive IIA on $Li_4\times M_6$
  9. No-go Argument for Nearly Kähler Compactifications
  10. Adding Orientifold Plane
  11. Conclusion and Discussion
  12. Conclusions: No-go Theorems for Lifshitz-like Spacetime in Supergravities
  13. Summary of the No-go Setups
  14. Why String Duals of Lifshitz-like Points are Hard