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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2019)135 |
| _version_ | 1818453610827087872 |
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| author | Nicolás Del Grosso Alan Garbarz Gabriel Palau Guillem Pérez-Nadal |
| author_facet | Nicolás Del Grosso Alan Garbarz Gabriel Palau Guillem Pérez-Nadal |
| author_sort | Nicolás Del Grosso |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-14T21:41:44Z |
| format | Article |
| id | doaj.art-27bb71a9f2f044edaaa8fedfa7e2ab06 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T21:41:44Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-27bb71a9f2f044edaaa8fedfa7e2ab062022-12-21T22:46:26ZengSpringerOpenJournal 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 |
| 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 |
| title | 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_short | Boundary-to-bulk maps for AdS causal wedges and RG flow |
| title_sort | boundary to bulk maps for ads causal wedges and rg flow |
| topic | AdS-CFT Correspondence Renormalization Group Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP10(2019)135 |
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