General Relativity and Gravitation

, Volume 43, Issue 5, pp 1391–1400 | Cite as

Anisotropic conformal infinity

  • Petr Hořava
  • Charles M. Melby-Thompson
Open Access
Research Article


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 Schrödinger 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.


AdS/CFT correspondence Holography for nonrelativistic field theories Lifshitz and Schrödinger spacetimes Conformal infinity of spacetime Anisotropic scaling 



We wish to thank Stéphane Detournay for useful discussions. The results presented in this paper were announced by one of us (PH) at Strings 2009 in Rome (June 2009), and at the Quantum Criticality and AdS/CFT Correspondence Miniprogram at KITP, Santa Barbara (July 2009); PH wishes to thank the orgainzers for their hospitality. This work has been supported by NSF Grants PHY-0555662 and PHY-0855653, DOE Grant DE-AC02-05CH11231, and by the Berkeley Center for Theoretical Physics.

Open Access

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Berkeley Center for Theoretical Physics, Department of PhysicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Theoretical Physics GroupLawrence Berkeley National LaboratoryBerkeleyUSA

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