### Abstract

We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be non-zero.

Original language | English |
---|---|

Pages (from-to) | 65-72 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 679 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 Aug 10 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Non-relativistic holography and singular black hole.** / Lin, Feng-Li; Wu, Shang Yu.

Research output: Contribution to journal › Article

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 679, no. 1, pp. 65-72. https://doi.org/10.1016/j.physletb.2009.07.002

}

TY - JOUR

T1 - Non-relativistic holography and singular black hole

AU - Lin, Feng-Li

AU - Wu, Shang Yu

PY - 2009/8/10

Y1 - 2009/8/10

N2 - We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be non-zero.

AB - We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be non-zero.

UR - http://www.scopus.com/inward/record.url?scp=67949102253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67949102253&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2009.07.002

DO - 10.1016/j.physletb.2009.07.002

M3 - Article

AN - SCOPUS:67949102253

VL - 679

SP - 65

EP - 72

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1

ER -