We develop in detail the holographic framework for an $$ \mathcal{N} $$ = 2 pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding super- conformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super- AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.
{ "_oai": { "updated": "2021-05-27T01:50:25Z", "id": "oai:repo.scoap3.org:60161", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Italy", "value": "DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, I-10129, Italy", "organization": "DISAT, Politecnico di Torino" }, { "country": "Italy", "value": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Turin, Italy", "organization": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino" }, { "country": "Italy", "value": "Arnold-Regge Center, Via P. Giuria 1, Turin, 10125, Italy", "organization": "Arnold-Regge Center" } ], "surname": "Andrianopoli", "email": "laura.andrianopoli@polito.it", "full_name": "Andrianopoli, L.", "given_names": "L." }, { "affiliations": [ { "country": "Italy", "value": "DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, I-10129, Italy", "organization": "DISAT, Politecnico di Torino" }, { "country": "Italy", "value": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Turin, Italy", "organization": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino" }, { "country": "Italy", "value": "Arnold-Regge Center, Via P. Giuria 1, Turin, 10125, Italy", "organization": "Arnold-Regge Center" }, { "country": "Italy", "value": "Centro Ricerche \u201cEnrico Fermi\u201d, Piazza del Viminale, 1, Rome, I-00184, Italy", "organization": "Centro Ricerche \u201cEnrico Fermi\u201d" } ], "surname": "Cerchiai", "email": "bianca.cerchiai@polito.it", "full_name": "Cerchiai, B.", "given_names": "B." }, { "affiliations": [ { "country": "Italy", "value": "DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, I-10129, Italy", "organization": "DISAT, Politecnico di Torino" }, { "country": "Italy", "value": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Turin, Italy", "organization": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino" } ], "surname": "Matrecano", "email": "riccardo.matrecano@polito.it", "full_name": "Matrecano, R.", "given_names": "R." }, { "affiliations": [ { "country": "Chile", "value": "Instituto de F\u00edsica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Casilla, Valpara\u00edso, 4059, Chile", "organization": "Pontificia Universidad Cat\u00f3lica de Valpara\u00edso" } ], "surname": "Miskovic", "email": "olivera.miskovic@pucv.cl", "full_name": "Miskovic, O.", "given_names": "O." }, { "affiliations": [ { "country": "Italy", "value": "DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, I-10129, Italy", "organization": "DISAT, Politecnico di Torino" }, { "country": "Italy", "value": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Turin, Italy", "organization": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino" } ], "surname": "Noris", "email": "ruggero.noris@polito.it", "full_name": "Noris, R.", "given_names": "R." }, { "affiliations": [ { "country": "Chile", "value": "Departamento de Ciencias F\u00edsicas, Universidad Andres Bello, Sazi\u00e9 2212, Piso 7, Santiago, Chile", "organization": "Universidad Andres Bello" } ], "surname": "Olea", "email": "rodrigo.olea@unab.cl", "full_name": "Olea, R.", "given_names": "R." }, { "affiliations": [ { "country": "Italy", "value": "DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, I-10129, Italy", "organization": "DISAT, Politecnico di Torino" }, { "country": "Italy", "value": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Turin, Italy", "organization": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino" } ], "surname": "Ravera", "email": "lucrezia.ravera@polito.it", "full_name": "Ravera, L.", "given_names": "L." }, { "affiliations": [ { "country": "Italy", "value": "DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, I-10129, Italy", "organization": "DISAT, Politecnico di Torino" }, { "country": "Italy", "value": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Turin, Italy", "organization": "Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino" }, { "country": "Italy", "value": "Arnold-Regge Center, Via P. Giuria 1, Turin, 10125, Italy", "organization": "Arnold-Regge Center" } ], "surname": "Trigiante", "email": "mario.trigiante@polito.it", "full_name": "Trigiante, M.", "given_names": "M." } ], "titles": [ { "source": "Springer", "title": "<math> <mi>N</mi> </math> $$ \\mathcal{N} $$ = 2 AdS4 supergravity, holography and Ward identities" } ], "dois": [ { "value": "10.1007/JHEP02(2021)141" } ], "publication_info": [ { "page_end": "70", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2021", "artid": "JHEP02(2021)141", "year": 2021, "page_start": "1", "journal_issue": "2" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-05-27T00:30:56.290224", "source": "Springer", "method": "Springer", "submission_number": "abbf0a02be8211eb92440a580a640a05" }, "page_nr": [ 70 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2021" } ], "control_number": "60161", "record_creation_date": "2021-02-18T04:30:15.515782", "_files": [ { "checksum": "md5:cfc34597d997870c58078ca95bda1b01", "filetype": "xml", "bucket": "4df7f759-6a7d-4f9d-936a-97dd71dad216", "version_id": "972f3bd1-b945-4bdd-ad0f-f54a40c1cbb7", "key": "10.1007/JHEP02(2021)141.xml", "size": 18272 }, { "checksum": "md5:8bc124e55a0bf6170cce1d98f608775b", "filetype": "pdf/a", "bucket": "4df7f759-6a7d-4f9d-936a-97dd71dad216", "version_id": "e68c0e4d-3cd9-4679-b9eb-33170cc0464b", "key": "10.1007/JHEP02(2021)141_a.pdf", "size": 974510 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "gr-qc" ], "value": "2010.02119" } ], "abstracts": [ { "source": "Springer", "value": "We develop in detail the holographic framework for an <math> <mi>N</mi> </math> $$ \\mathcal{N} $$ = 2 pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding super- conformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super- AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term." } ], "imprints": [ { "date": "2021-02-17", "publisher": "Springer" } ] }