Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

Thomas Faulkner, Hong Liu, Mukund Rangamani

Research output: Contribution to journalArticlepeer-review


We formulate a holographic Wilsonian renormalization group ow for strongly coupled systems with a gravity dual, motivated by the need to extract effciently 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.

Original languageEnglish (US)
Article number51
JournalJournal of High Energy Physics
Issue number8
StatePublished - 2011
Externally publishedYes


  • AdS-CFT correspondence
  • Gauge-gravity correspondence
  • Holography and condensed matter physics (AdS/CMT)
  • Renormalization group

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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