We study the OPE coefficients c Δ, J for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension Δ L in an AdS black hole. We verify that the OPE coefficient c d,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energy-momentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer Δ L , although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients γ Δ,J of the log(z $$ \overline{z} $$ ) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for γ Δ,J . We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with Δ L = d − 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient c d−2,0. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how c d,0 can be nonzero with exchanging scalar operators in these backgrounds.
{ "_oai": { "updated": "2019-12-25T21:31:16Z", "id": "oai:repo.scoap3.org:49578", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "China", "value": "Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China", "organization": "Tianjin University" } ], "surname": "Li", "email": "liyuezhou@tju.edu.cn", "full_name": "Li, Yue-Zhou", "given_names": "Yue-Zhou" }, { "affiliations": [ { "country": "China", "value": "Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China", "organization": "Tianjin University" } ], "surname": "Mai", "email": "zhanfeng.mai@gmail.com", "full_name": "Mai, Zhan-Feng", "given_names": "Zhan-Feng" }, { "affiliations": [ { "country": "China", "value": "Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China", "organization": "Tianjin University" } ], "surname": "L\u00fc", "email": "mrhonglu@gmail.com", "full_name": "L\u00fc, H.", "given_names": "H." } ], "titles": [ { "source": "Springer", "title": "Holographic OPE coefficients from AdS black holes with matters" } ], "dois": [ { "value": "10.1007/JHEP09(2019)001" } ], "publication_info": [ { "page_end": "43", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2019", "artid": "JHEP09(2019)001", "year": 2019, "page_start": "1", "journal_issue": "9" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2019-12-25T22:30:50.699467", "source": "Springer", "method": "Springer", "submission_number": "b483b9ac275d11eaad1402163e01809a" }, "page_nr": [ 43 ], "license": [ { "url": "https://creativecommons.org/licenses/by/3.0", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2019" } ], "control_number": "49578", "record_creation_date": "2019-09-06T05:30:22.929504", "_files": [ { "checksum": "md5:7f81bbe586ef08571c93ec1506087fec", "filetype": "xml", "bucket": "e8d1c619-a493-407f-9653-d7ed4ab3bad7", "version_id": "1a952681-0c17-4161-9380-0833badef921", "key": "10.1007/JHEP09(2019)001.xml", "size": 12544 }, { "checksum": "md5:7ea6dea08d241bb4048286610f081467", "filetype": "pdf/a", "bucket": "e8d1c619-a493-407f-9653-d7ed4ab3bad7", "version_id": "7a8eab82-5480-4145-88b8-9b52a32fdcb4", "key": "10.1007/JHEP09(2019)001_a.pdf", "size": 664102 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "1905.09302" } ], "abstracts": [ { "source": "Springer", "value": "We study the OPE coefficients c \u0394, J for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension \u0394 L in an AdS black hole. We verify that the OPE coefficient c d,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energy-momentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer \u0394 L , although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients \u03b3 \u0394,J of the log(z <math> <mover> <mi>z</mi> <mo>\u00af</mo> </mover> </math> $$ \\overline{z} $$ ) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for \u03b3 \u0394,J . We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with \u0394 L = d \u2212 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient c d\u22122,0. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how c d,0 can be nonzero with exchanging scalar operators in these backgrounds." } ], "imprints": [ { "date": "2019-12-25", "publisher": "Springer" } ] }