Instantons on Sasakian 7-manifolds

Instantons on Sasakian 7-manifolds

We study a natural contact instanton (CI) equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related both to the transverse Hermitian Yang-Mills (tHYM) condition and the G_2-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the modu...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2023-04
Hauptverfasser: Portilla, Luis E, Sá Earp, Henrique N
Format: Artikel
Sprache:eng
Schlagworte:
Instantons
Mathematics - Differential Geometry
Smoothness
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Portilla, Luis E
Sá Earp, Henrique N
description We study a natural contact instanton (CI) equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related both to the transverse Hermitian Yang-Mills (tHYM) condition and the G_2-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the moduli space of irreducible solutions. We derive cohomological conditions for smoothness, and we express its dimension in terms of the index of a transverse elliptic operator. Finally we show that the moduli space of selfdual contact instantons (ASDI) is K\"ahler, in the Sasakian case. As an instance of concrete interest, we specialise to transversely holomorphic Sasakian bundles over contact Calabi-Yau 7-manifolds, and we show that, in this context, the notions of contact instanton, integrable G_2-instanton and HYM connection coincide.
doi_str_mv 10.48550/arxiv.1906.11334
format Article
fullrecord <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1906_11334</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2248799048</sourcerecordid><originalsourceid>FETCH-LOGICAL-a954-a9a116d336bae655af19feeb556de29d102f6b5d90ae702115bcc574f519288e3</originalsourceid><addsrcrecordid>eNotj01PwzAQRC0kJKrSH9ATEZwTvGuvYx9RxUelShzae7RpbCmldUqcIvj3hJbLzOVpNE-IOchCWyL5yP13-1WAk6YAUEpfiQkqBbnViDdiltJOSommRCI1EffLmAaOQxdT1sVszYk_Wo5ZmR84tqHbN-lWXAfeJz_776nYvDxvFm_56v11uXha5exIj8EAplHK1OwNEQdwwfuayDQeXQMSg6mpcZJ9KRGA6u2WSh0IHFrr1VTcXWbPAtWxbw_c_1R_ItVZZCQeLsSx7z5PPg3Vrjv1cfxUIWpbOie1Vb-yRUl9</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2248799048</pqid></control><display><type>article</type><title>Instantons on Sasakian 7-manifolds</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Portilla, Luis E ; Sá Earp, Henrique N</creator><creatorcontrib>Portilla, Luis E ; Sá Earp, Henrique N</creatorcontrib><description>We study a natural contact instanton (CI) equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related both to the transverse Hermitian Yang-Mills (tHYM) condition and the G_2-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the moduli space of irreducible solutions. We derive cohomological conditions for smoothness, and we express its dimension in terms of the index of a transverse elliptic operator. Finally we show that the moduli space of selfdual contact instantons (ASDI) is K\"ahler, in the Sasakian case. As an instance of concrete interest, we specialise to transversely holomorphic Sasakian bundles over contact Calabi-Yau 7-manifolds, and we show that, in this context, the notions of contact instanton, integrable G_2-instanton and HYM connection coincide.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1906.11334</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Instantons ; Mathematics - Differential Geometry ; Smoothness</subject><ispartof>arXiv.org, 2023-04</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,781,882,27906</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.1906.11334$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1093/qmath/haad011$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Portilla, Luis E</creatorcontrib><creatorcontrib>Sá Earp, Henrique N</creatorcontrib><title>Instantons on Sasakian 7-manifolds</title><title>arXiv.org</title><description>We study a natural contact instanton (CI) equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related both to the transverse Hermitian Yang-Mills (tHYM) condition and the G_2-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the moduli space of irreducible solutions. We derive cohomological conditions for smoothness, and we express its dimension in terms of the index of a transverse elliptic operator. Finally we show that the moduli space of selfdual contact instantons (ASDI) is K\"ahler, in the Sasakian case. As an instance of concrete interest, we specialise to transversely holomorphic Sasakian bundles over contact Calabi-Yau 7-manifolds, and we show that, in this context, the notions of contact instanton, integrable G_2-instanton and HYM connection coincide.</description><subject>Instantons</subject><subject>Mathematics - Differential Geometry</subject><subject>Smoothness</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj01PwzAQRC0kJKrSH9ATEZwTvGuvYx9RxUelShzae7RpbCmldUqcIvj3hJbLzOVpNE-IOchCWyL5yP13-1WAk6YAUEpfiQkqBbnViDdiltJOSommRCI1EffLmAaOQxdT1sVszYk_Wo5ZmR84tqHbN-lWXAfeJz_776nYvDxvFm_56v11uXha5exIj8EAplHK1OwNEQdwwfuayDQeXQMSg6mpcZJ9KRGA6u2WSh0IHFrr1VTcXWbPAtWxbw_c_1R_ItVZZCQeLsSx7z5PPg3Vrjv1cfxUIWpbOie1Vb-yRUl9</recordid><startdate>20230412</startdate><enddate>20230412</enddate><creator>Portilla, Luis E</creator><creator>Sá Earp, Henrique N</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230412</creationdate><title>Instantons on Sasakian 7-manifolds</title><author>Portilla, Luis E ; Sá Earp, Henrique N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a954-a9a116d336bae655af19feeb556de29d102f6b5d90ae702115bcc574f519288e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Instantons</topic><topic>Mathematics - Differential Geometry</topic><topic>Smoothness</topic><toplevel>online_resources</toplevel><creatorcontrib>Portilla, Luis E</creatorcontrib><creatorcontrib>Sá Earp, Henrique N</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Portilla, Luis E</au><au>Sá Earp, Henrique N</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Instantons on Sasakian 7-manifolds</atitle><jtitle>arXiv.org</jtitle><date>2023-04-12</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>We study a natural contact instanton (CI) equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related both to the transverse Hermitian Yang-Mills (tHYM) condition and the G_2-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the moduli space of irreducible solutions. We derive cohomological conditions for smoothness, and we express its dimension in terms of the index of a transverse elliptic operator. Finally we show that the moduli space of selfdual contact instantons (ASDI) is K\"ahler, in the Sasakian case. As an instance of concrete interest, we specialise to transversely holomorphic Sasakian bundles over contact Calabi-Yau 7-manifolds, and we show that, in this context, the notions of contact instanton, integrable G_2-instanton and HYM connection coincide.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1906.11334</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2023-04
issn 2331-8422
language eng
recordid cdi_arxiv_primary_1906_11334
source arXiv.org; Free E- Journals
subjects Instantons
Mathematics - Differential Geometry
Smoothness
title Instantons on Sasakian 7-manifolds
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T00%3A15%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Instantons%20on%20Sasakian%207-manifolds&rft.jtitle=arXiv.org&rft.au=Portilla,%20Luis%20E&rft.date=2023-04-12&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1906.11334&rft_dat=%3Cproquest_arxiv%3E2248799048%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2248799048&rft_id=info:pmid/&rfr_iscdi=true