Journal of High Energy Physics

, 2019:135 | Cite as

Boundary-to-bulk maps for AdS causal wedges and RG flow

  • Nicolás Del Grosso
  • Alan GarbarzEmail author
  • Gabriel Palau
  • Guillem Pérez-Nadal
Open Access
Regular Article - Theoretical Physics


We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdSd+1 down to the unitary bound ∆ = (d − 2)/2. That is to say, we construct the ‘smearing functions’ K of HKLL but with different boundary conditions where both dimensions ∆+ and ∆ are taken into account. More precisely, we impose Robin boundary conditions, which interpolate between Dirichlet and Neumann boundary conditions and we give explicit expressions for the distributional kernel K with spacelike support. This flow between boundary conditions is known to be captured in the boundary by adding a double-trace deformation to the CFT. Indeed, we explicitly show that using K there is a consistent and explicit map from a Wightman function of the boundary QFT to a Wightman function of the bulk theory. In order to accomplish this we have to study first the microlocal properties of the boundary two-point function of the perturbed CFT and prove its wavefront set satisfies the microlocal spectrum condition. This permits to assert that K and the boundary two-point function can be multiplied as distributions.


AdS-CFT Correspondence Renormalization Group Conformal Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Physics Department, University of Buenos AiresBuenos AiresArgentina
  2. 2.IFIBA-ConicetBuenos AiresArgentina

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