In this work we extend the well-known spectral cover construction first developed by Friedman, Morgan, and Witten to describe more general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form, but can rather contain fibral divisors or multiple sections (i.e. a higher rank Mordell-Weil group). In these cases, general vector bundles defined over such Calabi-Yau manifolds cannot be described by ordinary spectral data. To accomplish this we employ well established tools from the mathematics literature of Fourier-Mukai functors. We also generalize existing tools for explicitly computing Fourier-Mukai transforms of stable bundles on elliptic Calabi-Yau manifolds. As an example of these new tools we produce novel examples of chirality changing small instanton transitions. The goal of this work is to provide a geometric formalism that can substantially increase the understood regimes of heterotic/F-theory duality.
{ "license": [ { "url": "http://creativecommons.org/licenses/by/3.0/", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Authors", "statement": "The Authors", "year": "2020" } ], "control_number": "53592", "_oai": { "updated": "2020-07-14T16:09:11Z", "id": "oai:repo.scoap3.org:53592", "sets": [ "NPB" ] }, "authors": [ { "affiliations": [ { "country": "USA", "value": "Department of Physics, Virginia Tech, Blacksburg, USA" } ], "surname": "Anderson", "email": "lara.anderson@vt.edu", "full_name": "Anderson, Lara B.", "given_names": "Lara B." }, { "affiliations": [ { "country": "China", "value": "College of Physics, Sichuan University, Chengdu, China" } ], "surname": "Gao", "email": "xingao@scu.edu.cn", "full_name": "Gao, Xin", "given_names": "Xin" }, { "affiliations": [ { "country": "USA", "value": "Department of Physics, Virginia Tech, Blacksburg, USA" } ], "surname": "Karkheiran", "email": "mohsenka@vt.edu", "full_name": "Karkheiran, Mohsen", "given_names": "Mohsen" } ], "_files": [ { "checksum": "md5:dad72251650edc043362d9211150d81b", "filetype": "xml", "bucket": "63a6b297-6087-4c1b-b883-065597220b65", "version_id": "faca012e-2721-478d-9076-c5fee93b0628", "key": "10.1016/j.nuclphysb.2020.115003.xml", "size": 863534 }, { "checksum": "md5:7143c00a6cb6528dd79fde2591b6a35e", "filetype": "pdf", "bucket": "63a6b297-6087-4c1b-b883-065597220b65", "version_id": "d347c1b2-132e-4647-a896-431caf3c7c2f", "key": "10.1016/j.nuclphysb.2020.115003.pdf", "size": 723593 }, { "checksum": "md5:db0a3e3b5d28058259d313271c27e0f3", "filetype": "pdf/a", "bucket": "63a6b297-6087-4c1b-b883-065597220b65", "version_id": "8bf526de-2e9e-438b-8653-4d3b7759c0b1", "key": "10.1016/j.nuclphysb.2020.115003_a.pdf", "size": 983629 } ], "record_creation_date": "2020-03-31T17:30:14.863588", "titles": [ { "source": "Elsevier", "title": "Extending the geometry of heterotic spectral cover constructions" } ], "collections": [ { "primary": "Nuclear Physics B" } ], "dois": [ { "value": "10.1016/j.nuclphysb.2020.115003" } ], "publication_info": [ { "journal_volume": "956 C", "journal_title": "Nuclear Physics B", "material": "article", "artid": "115003", "year": 2020 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "abstracts": [ { "source": "Elsevier", "value": "In this work we extend the well-known spectral cover construction first developed by Friedman, Morgan, and Witten to describe more general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form, but can rather contain fibral divisors or multiple sections (i.e. a higher rank Mordell-Weil group). In these cases, general vector bundles defined over such Calabi-Yau manifolds cannot be described by ordinary spectral data. To accomplish this we employ well established tools from the mathematics literature of Fourier-Mukai functors. We also generalize existing tools for explicitly computing Fourier-Mukai transforms of stable bundles on elliptic Calabi-Yau manifolds. As an example of these new tools we produce novel examples of chirality changing small instanton transitions. The goal of this work is to provide a geometric formalism that can substantially increase the understood regimes of heterotic/F-theory duality." } ], "imprints": [ { "date": "2020-07-14", "publisher": "Elsevier" } ], "acquisition_source": { "date": "2020-07-14T17:56:58.316220", "source": "Elsevier", "method": "Elsevier", "submission_number": "711475e0c5ea11ea825402163e01809a" } }