TY - JOUR

T1 - Non-relativistic holography and singular black hole

AU - Lin, Feng Li

AU - Wu, Shang Yu

N1 - Funding Information:
We would like to thank Chi-Wei Wang who participated the project at its early stage. We thank Jiunn-Wei Chen, Veronika Hubeny, Wei Li, Shin Nakamura, Mukund Rangamani, Sang-Jin Sin, Ta-Sheng Tai, Wen-Yu Wen, Piljin Yi and K.P. Yogendran for helpful comments and discussions. F.L.L. also likes to thank for the hospitality of KIAS and IPMU where part of the work is completed. This work was supported by Taiwan's NSC grant 96-2112-M-003-014 and by NCTS.

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.

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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 -