Anisotropic Conformal Infinity

TL;DR

This paper extends the concept of conformal infinity to anisotropic spacetimes, facilitating better understanding of holographic dualities in nonrelativistic and anisotropic gravity models.

Contribution

It introduces a generalized framework for anisotropic conformal infinity applicable to various spacetimes with asymptotic anisotropy, including Lifshitz and Schrödinger geometries.

Findings

Provides a new approach to holographic renormalization for anisotropic spacetimes

Applies the framework to Lifshitz, Schrödinger, warped AdS_3, and Kerr geometries

Enhances understanding of nonrelativistic holography and anisotropic gravity models

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.