欢迎来到天天文库
浏览记录
ID:39910369
大小:318.51 KB
页数:31页
时间:2019-07-14
《Borcherds symmetries in M-theory》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、PreprinttypesetinJHEPstyle-HYPERVERSIONLPT-ENS-02/20hep-th/0203070BorcherdssymmetriesinM-theoryDedicatedtoPr.S.Hawkingonhis60thbirthday.PierreHenry-Labord`ere,BernardJuliaandLouisPaulotLaboratoiredePhysiqueTh´eoriquedel’EcoleNormaleSup´erieure∗24rueLhomond,75231ParisCedex05,F
2、rancephenry@lpt.ens.frbernard.julia@lpt.ens.frpaulot@lpt.ens.frAbstract:ItiswellknownbutrathermysteriousthatrootspacesoftheEkLiegroupsappearinthesecondintegralcohomologyofregular,complex,compact,delPezzosurfaces.Thecorrespondinggroupsactonthescalarfields(0-forms)oftoroidalcomp
3、actificationsofMtheory.TheirBorelsubgroupsareactuallysubgroupsofsupergroupsoffinitedimensionovertheGrassmannalgebraofdifferentialformsonspacetimethathavebeenshowntopreservetheself-dualityequationobeyedbyallbosonicform-fieldsofthetheory.Weshowherethatthecorrespondingdualitysuperal
4、gebrasarenothingbutBorcherdssuperalgebrastruncatedbytheabovechoiceofGrassmanncoefficients.ThefullBorcherds’rootlatticesarethesecondintegralcohomologyofthedelPezzosurfaces.OurchoiceofsimplerootsarXiv:hep-th/0203070v27May2002usestheanti-canonicalformanditsknownorthogonalcomplemen
5、t.AnotherresultisthedeterminationofdelPezzosurfacesassociatedtootherstringandfieldtheorymodels.DimensionalreductiononTkcorrespondstoblow-upofkpointsingeneralpositionwithrespecttoeachother.AlltheoriesoftheMagictrianglethatreducetotheEnsigmamodelinthreedimensionscorrespondtosing
6、ulardelPezzosurfaceswithA8−n(normal)singularityatapoint.ThecaseoftypeIandheterotictheoriesifonedropstheirgaugesectorcorrespondstonon-normal(singularalongacurve)delPezzo’s.WecommentonpreviousencounterswithBorcherdsalgebrasattheendofthepaper.∗UMR8549duCentreNationaldelaRecherch
7、eScientifiqueetdel’EcoleNormaleSup´erieure´Contents1.Introduction22.Geometricalprerequisites32.1Divisorsandtheirclasses32.2Intersectiononalgebraicsurfaces42.3Ampledivisors,projectiveembeddingsanddegrees42.4CanonicalclassKX42.5Blowinguppoints53.FromdelPezzosurfacestoBorcherdssu
8、peralgebras54.SmoothdelPezzo’s74.1Mtheory74.2IIAtheory104.3IIBtheory
此文档下载收益归作者所有