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Journal of High Energy Physics

, 2013:115 | Cite as

Holographic interpretations of the renormalization group

  • Vijay Balasubramanian
  • Monica Guica
  • Albion LawrenceEmail author
Open Access
Article

Abstract

In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension \( \varDelta \notin \frac{d}{2}+\mathbb{Z} \), for sufficiently low momenta. We then clarify the relation between the saddle point approximation to the Wilsonian effective action (S W ) and boundary conditions at a cutoff surface in AdS space. In particular, we interpret non-local multi-trace operators in S W as arising in Lorentzian AdS space from the temporary passage of excitations through the UV region that has been integrated out. Coarse-graining these operators makes the action effectively local.

Keywords

Gauge-gravity correspondence AdS-CFT Correspondence Renormalization Group 

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Copyright information

© SISSA 2013

Authors and Affiliations

  • Vijay Balasubramanian
    • 1
    • 2
  • Monica Guica
    • 1
  • Albion Lawrence
    • 3
    Email author
  1. 1.David Rittenhouse LaboratoryUniversity of PennsylvaniaPhiladelphiaU.S.A.
  2. 2.Laboratoire de Physique ThéoriqueÉcole Normale SupérieureParisFrance
  3. 3.Martin Fisher School of PhysicsBrandeis UniversityWalthamU.S.A.

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