Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

Details Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

2010-10-19

arxiv.org/abs/1010.4036v2

JHEP 1108:051,2011

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 2 figures; references added, minor changes

Scientific paper

10.1007/JHEP08(2011)051

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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