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Integrating out geometry: holographic Wilsonian RG and the membrane paradigm

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Abstract

We formulate a holographic Wilsonian renormalization group flow for strongly coupled systems with a gravity dual, motivated by the need to extract efficiently low energy behavior of such systems. Starting with field theories defined on a cut-off surface in a bulk spacetime, we propose that integrating out high energy modes in the field theory should correspond to integrating out a part of the bulk geometry. We describe how to carry out this procedure in practice in the classical gravity approximation using examples of scalar and vector fields. By integrating out bulk degrees of freedom all the way to a black hole horizon, this formulation defines a refined version of the black hole membrane paradigm. Furthermore, it also provides a derivation of the semi-holographic description of low energy physics.

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Authors and Affiliations

  1. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    Thomas Faulkner

  2. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Hong Liu

  3. Centre for Particle Theory & Department of Mathematical Sciences, Science Laboratories, South Road, Durham, DH1 3LE, U.K.

    Mukund Rangamani

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  1. Thomas Faulkner
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  2. Hong Liu
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  3. Mukund Rangamani
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Correspondence to Mukund Rangamani.

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ArXiv ePrint: 1010.4036

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Faulkner, T., Liu, H. & Rangamani, M. Integrating out geometry: holographic Wilsonian RG and the membrane paradigm. J. High Energ. Phys. 2011, 51 (2011). https://doi.org/10.1007/JHEP08(2011)051

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