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Anisotropic Conformal Infinity

Petr Horava, Charles M. Melby-Thompson

Abstract

We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrodinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.

Anisotropic Conformal Infinity

Abstract

We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrodinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.

Paper Structure

This paper contains 11 sections, 29 equations.

Table of Contents

  1. Introduction
  2. Anisotropic Conformal Infinity: The Spatially Isotropic Case
  3. The main idea
  4. Asymptotic structure of the Lifshitz space
  5. Spatially Anisotropic Conformal Infinity
  6. Asymptotic structure of null warped $AdS_3$
  7. Asymptotic structure of the Schrödinger space
  8. Holographic Renormalization and Anisotropic Conformal Infinity
  9. The general prescription
  10. Asymptotic structure of spacelike warped $AdS_3$
  11. Conclusions