This paper focuses on the analysis of 4 d N $$ \mathcal{N} $$ = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 1 2 $$ \frac{1}{2} $$ -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4 d N $$ \mathcal{N} $$ = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4 d N $$ \mathcal{N} $$ = 4 superconformal theories with a line defect, 3 d N $$ \mathcal{N} $$ = 4 superconformal theories with no defect, and OSP(4 ∗ |4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions.
{ "_oai": { "updated": "2018-04-30T21:55:54Z", "id": "oai:repo.scoap3.org:18769" }, "authors": [ { "raw_name": "Liendo, Pedro", "affiliations": [ { "country": "Germany", "value": "IMIP, Humboldt-Universit\u00e4t zu Berlin, IRIS Adlershof, Zum Gro\u00dfen Windkanal 6, 12489, Berlin, Germany" } ], "surname": "Liendo", "given_names": "Pedro", "full_name": "Liendo, Pedro" }, { "raw_name": "Meneghelli, Carlo", "affiliations": [ { "country": "USA", "value": "Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794-3636, U.S.A." } ], "surname": "Meneghelli", "given_names": "Carlo", "full_name": "Meneghelli, Carlo" } ], "titles": [ { "source": "Springer/SISSA", "title": "Bootstrap equations for N $$ \\mathcal{N} $$ = 4 SYM with defects" } ], "dois": [ { "value": "10.1007/JHEP01(2017)122" } ], "publication_info": [ { "page_start": "122", "material": "article", "journal_title": "Journal of High Energy Physics", "year": 2017 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2017-01-28T00:00:00", "source": "Springer/SISSA", "method": "scoap3", "submission_number": "3e8107fa4cbc11e8b67702163e01809a" }, "page_nr": [ 48 ], "license": [ { "url": "http://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "The Author(s)" } ], "control_number": "18769", "record_creation_date": "2017-01-28T00:00:00", "_files": [ { "checksum": "md5:5a8b460e3f01f098281363e6cc45ca38", "filetype": "xml", "bucket": "6a80e314-a15e-43dc-ad39-7bf997d128d2", "version_id": "17b5a237-b992-466e-92d2-7e6ded428f44", "key": "10.1007/JHEP01(2017)122.xml", "size": 178788 }, { "checksum": "md5:1954ab09043c2bfdaf32e2d2e8aa34af", "filetype": "pdf/a", "bucket": "6a80e314-a15e-43dc-ad39-7bf997d128d2", "version_id": "14222ace-ce0a-477d-ae94-fbe79776db66", "key": "10.1007/JHEP01(2017)122_a.pdf", "size": 892578 } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "1608.05126" } ], "abstracts": [ { "source": "Springer/SISSA", "value": "This paper focuses on the analysis of 4 d N $$ \\mathcal{N} $$ = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 1 2 $$ \\frac{1}{2} $$ -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4 d N $$ \\mathcal{N} $$ = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4 d N $$ \\mathcal{N} $$ = 4 superconformal theories with a line defect, 3 d N $$ \\mathcal{N} $$ = 4 superconformal theories with no defect, and OSP(4 \u2217 |4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions." } ], "imprints": [ { "date": "2017-01-27", "publisher": "Springer/SISSA" } ] }