The square-root of Siegel modular forms of CHL orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for . We study the decomposition of these Siegel modular forms in terms of characters of two sub-algebras: one is a and the second is a Borcherds extension of the . This is a continuation of our previous work where we studied the case of Siegel modular forms appearing in the context of Umbral moonshine. This situation is more intricate and provides us with a new example (for ) that did not appear in that case. We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for .
{ "license": [ { "url": "http://creativecommons.org/licenses/by/3.0/", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "statement": "The Author(s)", "year": "2023" } ], "control_number": "75940", "_oai": { "updated": "2023-03-27T18:30:29Z", "id": "oai:repo.scoap3.org:75940", "sets": [ "NPB" ] }, "authors": [ { "surname": "Govindarajan", "given_names": "Suresh", "affiliations": [ { "country": "India", "value": "Department of Physics, Indian Institute of Technology Madras, Chennai, India" } ], "full_name": "Govindarajan, Suresh", "orcid": "0000-0002-0702-0288", "email": "suresh@physics.iitm.ac.in" }, { "affiliations": [ { "country": "India", "value": "The Institute of Mathematical Sciences, Chennai, India" }, { "country": "India", "value": "Homi Bhabha National Institute, Training School Complex, Mumbai, India" } ], "surname": "Shabbir", "email": "mshabbir@imsc.res.in", "full_name": "Shabbir, Mohammad", "given_names": "Mohammad" } ], "_files": [ { "checksum": "md5:a4afbc0bee643375b6010644bc53e25b", "filetype": "xml", "bucket": "64970285-13ce-4507-a330-6e0983116c8b", "version_id": "580d9a55-7082-4b51-aecf-72660182a75a", "key": "10.1016/j.nuclphysb.2023.116127.xml", "size": 544342 }, { "checksum": "md5:4ec2beadb1132f2b326f34daf591e360", "filetype": "pdf", "bucket": "64970285-13ce-4507-a330-6e0983116c8b", "version_id": "ceafa12d-dea2-4914-9cc2-659bc8aae2ac", "key": "10.1016/j.nuclphysb.2023.116127.pdf", "size": 384061 }, { "checksum": "md5:e53c9ce3072e84cbf06ac31cb19877dc", "filetype": "pdf/a", "bucket": "64970285-13ce-4507-a330-6e0983116c8b", "version_id": "cb4446b8-0896-4227-a98e-ac3ebd128eb4", "key": "10.1016/j.nuclphysb.2023.116127_a.pdf", "size": 384012 } ], "record_creation_date": "2023-02-22T15:30:21.627724", "titles": [ { "source": "Elsevier", "title": "Decomposition of denominator formulae of some BKM Lie superalgebras - II" } ], "collections": [ { "primary": "Nuclear Physics B" } ], "dois": [ { "value": "10.1016/j.nuclphysb.2023.116127" } ], "publication_info": [ { "journal_volume": "989 C", "journal_title": "Nuclear Physics B", "material": "article", "artid": "116127", "year": 2023 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "abstracts": [ { "source": "Elsevier", "value": "The square-root of Siegel modular forms of CHL <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>N</mi></mrow></msub></math> orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for <math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math>. We study the decomposition of these Siegel modular forms in terms of characters of two sub-algebras: one is a <math><mover><mrow><mi>s</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>\u02c6</mo></mrow></mover></math> and the second is a Borcherds extension of the <math><mover><mrow><mi>s</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>\u02c6</mo></mrow></mover></math>. This is a continuation of our previous work where we studied the case of Siegel modular forms appearing in the context of Umbral moonshine. This situation is more intricate and provides us with a new example (for <math><mi>N</mi><mo>=</mo><mn>5</mn></math>) that did not appear in that case. We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for <math><mi>N</mi><mo>=</mo><mn>5</mn><mo>,</mo><mn>6</mn></math>." } ], "imprints": [ { "date": "2023-02-21", "publisher": "Elsevier" } ], "acquisition_source": { "date": "2023-03-27T18:30:23.762253", "source": "Elsevier", "method": "Elsevier", "submission_number": "61d8ce0ecccd11eda920065bd8dc6b20" } }