We describe the projective superspace approach to supersymmetric models with off-shell (0, 4) supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables — one doublet for each SU(2) in the R-symmetry SU(2) × SU(2) which are interpreted as homogeneous coordinates on CP 1 × CP 1. The superfields are analytic in the CP 1 coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten’s ADHM sigma model — a linear sigma model with non-derivative interactions whose target is R 4 with a Yang-Mills instanton solution. The hyperkähler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction.
{ "_oai": { "updated": "2023-10-24T00:36:04Z", "id": "oai:repo.scoap3.org:78982", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "India", "value": "International Centre for Theoretical Sciences-TIFR, Shivakote, Bengaluru, 560089, India", "organization": "International Centre for Theoretical Sciences-TIFR" } ], "surname": "Prabhakar", "email": "naveen.s.prabhakar@gmail.com", "full_name": "Prabhakar, Naveen", "given_names": "Naveen" }, { "affiliations": [ { "country": "USA", "value": "C.N. Yang Institute of Theoretical Physics, Stony Brook University, Stony Brook, NY, 11794-3840, USA", "organization": "Stony Brook University" } ], "surname": "Ro\u010dek", "email": "martin.rocek@stonybrook.edu", "full_name": "Ro\u010dek, Martin", "given_names": "Martin" } ], "titles": [ { "source": "Springer", "title": "(0, 4) Projective superspaces. Part I. Interacting linear sigma models" } ], "dois": [ { "value": "10.1007/JHEP07(2023)117" } ], "publication_info": [ { "page_end": "50", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2023", "artid": "JHEP07(2023)117", "year": 2023, "page_start": "1", "journal_issue": "7" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-10-24T00:33:02.605219", "source": "Springer", "method": "Springer", "submission_number": "7734084a720411eea066664922b6a1d4" }, "page_nr": [ 50 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2023" } ], "control_number": "78982", "record_creation_date": "2023-07-14T18:30:08.955378", "_files": [ { "checksum": "md5:5f67a3111bd0e44eb1963e08bf2b99d4", "filetype": "xml", "bucket": "e86e9bcd-4840-4c23-aa0a-313e5599783a", "version_id": "63d8954f-c28f-44fc-8d0c-f1f018e78761", "key": "10.1007/JHEP07(2023)117.xml", "size": 11663 }, { "checksum": "md5:1a885baa3bad544cfdbb50838c1b41e3", "filetype": "pdf/a", "bucket": "e86e9bcd-4840-4c23-aa0a-313e5599783a", "version_id": "69f090cb-871a-419c-8d97-6d61344d7b5b", "key": "10.1007/JHEP07(2023)117_a.pdf", "size": 728879 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "math-ph", "math.MP" ], "value": "2303.14675" } ], "abstracts": [ { "source": "Springer", "value": "We describe the projective superspace approach to supersymmetric models with off-shell (0, 4) supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables \u2014 one doublet for each SU(2) in the R-symmetry SU(2) \u00d7 SU(2) which are interpreted as homogeneous coordinates on CP 1 \u00d7 CP 1. The superfields are analytic in the CP 1 coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten\u2019s ADHM sigma model \u2014 a linear sigma model with non-derivative interactions whose target is R 4 with a Yang-Mills instanton solution. The hyperk\u00e4hler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction." } ], "imprints": [ { "date": "2023-07-13", "publisher": "Springer" } ] }