It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the superconformal supergroups , , , . Roughly speaking, the super-Schwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach to superalgebra . The minimal set of constraints we used includes: (a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; (b) nullifying the form for dilatation. In contrast to the case, the new super-Schwarzian appears to be a component of the form for automorphism.
{ "_oai": { "updated": "2022-05-19T08:07:00Z", "id": "oai:repo.scoap3.org:69263", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Nikolay Kozyrev", "affiliations": [ { "country": "JINR", "value": "Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia" } ], "surname": "Kozyrev", "given_names": "Nikolay", "full_name": "Kozyrev, Nikolay" }, { "raw_name": "Sergey Krivonos", "affiliations": [ { "country": "JINR", "value": "Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia" } ], "surname": "Krivonos", "given_names": "Sergey", "full_name": "Krivonos, Sergey" } ], "titles": [ { "source": "APS", "title": "<math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Schwarzian with <math><mi>D</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mi>\u03b1</mi><mo>)</mo></math> symmetry" } ], "dois": [ { "value": "10.1103/PhysRevD.105.085010" } ], "publication_info": [ { "journal_volume": "105", "journal_title": "Physical Review D", "material": "article", "journal_issue": "8", "year": 2022 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2022-05-19T08:05:30.779094", "source": "APS", "method": "APS", "submission_number": "6bd14ca2d74a11eca1a1661ec451a4e4" }, "page_nr": [ 12 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2022" } ], "control_number": "69263", "record_creation_date": "2022-04-19T14:30:07.213500", "_files": [ { "checksum": "md5:22739fe2557434ecfb3c77f8c1ef1b03", "filetype": "pdf", "bucket": "8173e2a8-7075-4466-be90-ba76092dde3c", "version_id": "0fcd03c2-5f14-49db-b11f-6940de16f0d7", "key": "10.1103/PhysRevD.105.085010.pdf", "size": 262546 }, { "checksum": "md5:5fbde6049ed34db49f09ff932d84d8b0", "filetype": "xml", "bucket": "8173e2a8-7075-4466-be90-ba76092dde3c", "version_id": "23ee2b59-a1b5-47ff-aa2d-d2677cc32d61", "key": "10.1103/PhysRevD.105.085010.xml", "size": 388899 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "2112.14481" } ], "abstracts": [ { "source": "APS", "value": "It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the superconformal supergroups <math><mrow><mi>O</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>1</mn><mo>)</mo></mrow></math>, <math><mrow><mi>O</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>3</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>. Roughly speaking, the super-Schwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach to superalgebra <math><mi>D</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mi>\u03b1</mi><mo>)</mo></math>. The minimal set of constraints we used includes: (a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; (b) nullifying the form for dilatation. In contrast to the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math> case, the new super-Schwarzian appears to be a <math><mi>d</mi><msup><mi>\u03b8</mi><mrow><mi>i</mi><mi>a</mi></mrow></msup></math> component of the form for <math><mi>s</mi><mi>u</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> automorphism." } ], "imprints": [ { "date": "2022-04-19", "publisher": "APS" } ] }