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[{"key": "dc.contributor.author", "value": "M\u00e4kinen, Ilkka", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2011-12-16T09:03:28Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2011-12-16T09:03:28Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2011", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1190786", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/37094", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4 tutkielma on johdatus AdS/CFT-dualiteettiin. P\u00e4\u00e4asiallinen tavoitteeni on ollut\r\nymm\u00e4rt\u00e4\u00e4 se ajatusten ketju, joka alkaa tavallisesta kvanttikentt\u00e4teoriasta ja yleisest\u00e4\r\nsuhteellisuusteoriasta ja p\u00e4\u00e4tyy konjektuuriin, jonka mukaan tietyt s\u00e4ieteoriat\r\novat ekvivalentteja alempiulotteisten mittateorioiden kanssa. Dualiteetin sovellukset\r\nmallien rakentamisessa j\u00e4\u00e4v\u00e4t t\u00e4ss\u00e4 ty\u00f6ss\u00e4 v\u00e4h\u00e4lle huomiolle.\r\nKappale 1 sis\u00e4lt\u00e4\u00e4 katsauksen supersymmetriaan. Lyhyen historiallisen johdatuksen\r\nj\u00e4lkeen esittelemme supersymmetriamuunnosten algebran. T\u00e4m\u00e4n algebran esityksi\u00e4\r\ntutkimme sek\u00e4 abstraktein menetelmin ett\u00e4 tarkastelemalla esimerkki\u00e4 supersymmetrisest\u00e4\r\nkentt\u00e4teoriasta. T\u00e4m\u00e4n j\u00e4lkeen esittelemme superavaruusformalismin, ja\r\nn\u00e4yt\u00e4mme miten supersymmetriamuunnokset tulkitaan superavaruuden koordinaattimuunnoksina,\r\nja ett\u00e4 superavaruudessa m\u00e4\u00e4riteltyjen funktioiden integroiminen tuottaa\r\nsupersymmetrisi\u00e4 teorioita m\u00e4\u00e4rittelevi\u00e4 Lagrangen funktioita. N\u00e4yt\u00e4mme miten\r\nsuperavaruusformalismia k\u00e4ytet\u00e4\u00e4n supersymmetristen mittateorioiden, mm. supersymmetrisoidun\r\nQCD:n, rakentamiseen. Lopuksi tarkastelemme lyhyesti supersymmetrian\r\nspontaania rikkoutumista ja supersymmetristen kentt\u00e4teorioiden kvantisointia.\r\nKappaleessa 2 korotamme globaalit supersymmetriamuunnokset lokaaleiksi, p\u00e4\u00e4tyen\r\nt\u00e4t\u00e4 kautta supergravitaatioteorioihin. Esittelemme aluksi yleisen suhteellisuusteorian\r\nmonijalkamuotoilun (vielbein formulation), jonka k\u00e4ytt\u00e4minen on v\u00e4ltt\u00e4m\u00e4t\u00f6nt\u00e4\r\nspinorien tuomiseksi gravitaatioteoriaan. Sen j\u00e4lkeen perustelemme esimerkin avulla\r\nmiksi supersymmetrian korottaminen lokaaliksi tuo automaattisesti gravitaation\r\nosaksi teoriaa. K\u00e4sittelemme melko perusteellisesti niin sanotun yksinkertaisen neliulotteisen\r\nsupergravitaation. Tutkimme my\u00f6s, miten supersymmetria-algebra kuuluu\r\nyleist\u00e4\u00e4 korkeampiulotteisiin avaruusaikoihin. Kappaleen lopuksi kuvailemme 10- ja\r\n11- ulotteisia supergravitaatioteorioita ja niiden symmetrioita.\r\nKappaleiden 1 ja 2 sis\u00e4lt\u00e4mien tietojen avulla olemme valmiit esittelem\u00e4\u00e4n loput\r\nAdS/ CFT-dualiteetin rakenneosat kappaleessa 3. Annamme aluksi lyhyen johdatuksen\r\ns\u00e4ieteoriaan ja D-braaneihin. Toteamme, ett\u00e4 matalan energian rajalla s\u00e4ieteoriat\r\npalautuvat supergravitaatioteorioiksi. Tutkimme niin sanottua suuren N:n rajaa mittateorioissa,\r\nja perustelemme miksi suuren N:n kehitelm\u00e4n muoto viittaa mittateorioiden\r\nja s\u00e4ieteorioiden v\u00e4lill\u00e4 olevaan yhteyteen. Tarkastelemme kymmenulotteisen\r\nsupergravitaation p-braaniratkaisuja ja selit\u00e4mme, miten ne liittyv\u00e4t s\u00e4ieteorian Dbraaneihin.\r\nAnnamme katsauksen konformi-invariantteihin kentt\u00e4teorioihin, jonka j\u00e4lkeen\r\nolemme valmiit esittelem\u00e4\u00e4n Maldacenan konjektuurin AdS/CFT-dualiteetista.\r\nTarkastelemme avoimien s\u00e4ikeiden ja D-braanien muodostamaa systeemi\u00e4 kahdella eri\r\ntavalla, p\u00e4\u00e4tellen t\u00e4t\u00e4 kautta ett\u00e4 er\u00e4s neliulotteinen supersymmetrinen mittateoria\r\non todenn\u00e4k\u00f6isesti ekvivalentti tietyn viisiulotteisessa avaruudessa m\u00e4\u00e4ritellyn s\u00e4ieteorian\r\nkanssa. Esittelemme lyhyesti dualiteetin eri puolia, jonka j\u00e4lkeen lopetamme\r\ntutkielman tarkastelemalla lyhyesti, miten dualiteettia voidaan k\u00e4ytt\u00e4\u00e4 QCD:ta kuvaavien\r\nmallien rakentamiseen.", "language": "", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Ilkka M\u00e4kinen (ilsamaki) on 2011-12-16 09:03:28.301956. Form: Pro gradu -lomake (1 tekij\u00e4) (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake-1-tekijae). JyX data:", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija@noreply.fi) on 2011-12-16T09:03:28Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-2011121611809.pdf: 977420 bytes, checksum: 85b96edfa567bb7df2c7d48b31f4c401 (MD5)\r\nlicense.html: 4997 bytes, checksum: 049fb95404a06daf68d153591239cf8c (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2011-12-16T09:03:28Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-2011121611809.pdf: 977420 bytes, checksum: 85b96edfa567bb7df2c7d48b31f4c401 (MD5)\r\nlicense.html: 4997 bytes, checksum: 049fb95404a06daf68d153591239cf8c (MD5)\r\n Previous issue date: 2011", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "119 sivua", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "AdS/CFT", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Supersymmetry, supergravity and the AdS/CFT correspondence", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-2011121611809", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.dcmitype", "value": "Text", "language": "en", "element": "type", "qualifier": "dcmitype", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2011-12-16T09:03:29Z", "language": "", "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4021", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "supersymmetria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "gravitaatio", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "s\u00e4ieteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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