Boundary-to-bulk maps for AdS causal wedges and RG flow
Abstract We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS d+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 acc...
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Online Access: | http://link.springer.com/article/10.1007/JHEP10(2019)135 |
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doaj-27bb71a9f2f044edaaa8fedfa7e2ab062020-11-25T03:55:46ZengSpringerOpenJournal of High Energy Physics1029-84792019-10-0120191012910.1007/JHEP10(2019)135Boundary-to-bulk maps for AdS causal wedges and RG flowNicolás Del Grosso0Alan Garbarz1Gabriel Palau2Guillem Pérez-Nadal3Physics Department, University of Buenos AiresPhysics Department, University of Buenos AiresPhysics Department, University of Buenos AiresPhysics Department, University of Buenos AiresAbstract We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS d+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.http://link.springer.com/article/10.1007/JHEP10(2019)135AdS-CFT CorrespondenceRenormalization GroupConformal Field Theory |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nicolás Del Grosso Alan Garbarz Gabriel Palau Guillem Pérez-Nadal |
spellingShingle |
Nicolás Del Grosso Alan Garbarz Gabriel Palau Guillem Pérez-Nadal Boundary-to-bulk maps for AdS causal wedges and RG flow Journal of High Energy Physics AdS-CFT Correspondence Renormalization Group Conformal Field Theory |
author_facet |
Nicolás Del Grosso Alan Garbarz Gabriel Palau Guillem Pérez-Nadal |
author_sort |
Nicolás Del Grosso |
title |
Boundary-to-bulk maps for AdS causal wedges and RG flow |
title_short |
Boundary-to-bulk maps for AdS causal wedges and RG flow |
title_full |
Boundary-to-bulk maps for AdS causal wedges and RG flow |
title_fullStr |
Boundary-to-bulk maps for AdS causal wedges and RG flow |
title_full_unstemmed |
Boundary-to-bulk maps for AdS causal wedges and RG flow |
title_sort |
boundary-to-bulk maps for ads causal wedges and rg flow |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-10-01 |
description |
Abstract We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS d+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. |
topic |
AdS-CFT Correspondence Renormalization Group Conformal Field Theory |
url |
http://link.springer.com/article/10.1007/JHEP10(2019)135 |
work_keys_str_mv |
AT nicolasdelgrosso boundarytobulkmapsforadscausalwedgesandrgflow AT alangarbarz boundarytobulkmapsforadscausalwedgesandrgflow AT gabrielpalau boundarytobulkmapsforadscausalwedgesandrgflow AT guillempereznadal boundarytobulkmapsforadscausalwedgesandrgflow |
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1724468203964334080 |