# 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.

## Key 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.