We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions containing chiral operators in theories with N $$ \mathcal{N} $$ -extended supersymmetry. We also reproduce these results by extending the “shadow formalism” of Ferrara, Gatto, Grillo, and Parisi to supersymmetric theories, where superconformal blocks can be represented as superspace integrals of three-point functions multiplied by shadow three-point functions.
{ "_oai": { "updated": "2018-05-01T10:52:20Z", "id": "oai:repo.scoap3.org:3780" }, "authors": [ { "raw_name": "A. Liam Fitzpatrick", "affiliations": [ { "country": "USA", "value": "Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, U.S.A." } ], "surname": "Fitzpatrick", "given_names": "A. Liam", "full_name": "Fitzpatrick, A. Liam" }, { "raw_name": "Jared Kaplan", "affiliations": [ { "country": "USA", "value": "Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, U.S.A." } ], "surname": "Kaplan", "given_names": "Jared", "full_name": "Kaplan, Jared" }, { "raw_name": "Zuhair U. Khandker", "affiliations": [ { "country": "USA", "value": "Physics Department, Boston University, Boston, MA 02215, U.S.A." } ], "surname": "Khandker", "given_names": "Zuhair U.", "full_name": "Khandker, Zuhair U." }, { "raw_name": "Daliang Li", "affiliations": [ { "country": "USA", "value": "Department of Physics, Yale University, New Haven, CT 06520, U.S.A." } ], "surname": "Li", "given_names": "Daliang", "full_name": "Li, Daliang" }, { "raw_name": "David Poland", "affiliations": [ { "country": "USA", "value": "Department of Physics, Yale University, New Haven, CT 06520, U.S.A." } ], "surname": "Poland", "given_names": "David", "full_name": "Poland, David" }, { "raw_name": "David Simmons-Duffin", "affiliations": [ { "country": "USA", "value": "School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A." } ], "surname": "Simmons-Duffin", "given_names": "David", "full_name": "Simmons-Duffin, David" } ], "titles": [ { "source": "Springer/SISSA", "title": "Covariant approaches to superconformal blocks" } ], "dois": [ { "value": "10.1007/JHEP08(2014)129" } ], "publication_info": [ { "page_start": "129", "material": "article", "journal_title": "Journal of High Energy Physics", "year": 2014 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2014-08-26T00:00:00", "source": "Springer/SISSA", "method": "scoap3", "submission_number": "6f4b628e4d2711e8b67702163e01809a" }, "page_nr": [ 30 ], "license": [ { "url": "http://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "The Author(s)" } ], "control_number": "3780", "record_creation_date": "2014-08-26T00:00:00", "_files": [ { "checksum": "md5:4c206497707ae0a3500d6d640e8f3266", "filetype": "xml", "bucket": "94c6d6ec-3d63-4293-8db7-4cad7d03f791", "version_id": "df9bde9d-fde0-47dd-b70f-3732705215bb", "key": "10.1007/JHEP08(2014)129.xml", "size": 94319 }, { "checksum": "md5:a98b36f4e3b1bef5154350906e557425", "filetype": "pdf/a", "bucket": "94c6d6ec-3d63-4293-8db7-4cad7d03f791", "version_id": "adfbcc98-64c1-469a-89ff-32690bd10cdf", "key": "10.1007/JHEP08(2014)129_a.pdf", "size": 557106 } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "1402.1167" } ], "abstracts": [ { "source": "Springer/SISSA", "value": "We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions containing chiral operators in theories with N $$ \\mathcal{N} $$ -extended supersymmetry. We also reproduce these results by extending the \u201cshadow formalism\u201d of Ferrara, Gatto, Grillo, and Parisi to supersymmetric theories, where superconformal blocks can be represented as superspace integrals of three-point functions multiplied by shadow three-point functions." } ], "imprints": [ { "date": "2014-08-25", "publisher": "Springer/SISSA" } ] }