Supersymmetric geometries in string theory
<p>Supersymmetric vacua of string theory endow the internal space with a special geometric structure. We refer to these structures collectively as supersymmetric geometries. The objective of this thesis is to study two classes of supersymmetric geometries and their associated quantum field the...
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| Формат: | Дипломын ажил |
| Хэл сонгох: | English |
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2021
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| _version_ | 1826316468450492416 |
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| author | Cizel, S |
| author2 | Schafer-Nameki, S |
| author_facet | Schafer-Nameki, S Cizel, S |
| author_sort | Cizel, S |
| collection | OXFORD |
| description | <p>Supersymmetric vacua of string theory endow the internal space with a special geometric structure. We refer to these structures collectively as supersymmetric geometries. The objective of this thesis is to study two classes of supersymmetric geometries and their associated quantum field theories arising from string compactifications.</p>
<p>In the first part of this thesis, we study M-theory compactifications on G2- manifolds. We focus on the gauge sector of such compactifications by studying the Higgs bundle, characterizing a local ALE-fibration over a supersymmetric three-cycle M3, obtained from a partially twisted 7d super Yang-Mills theory on M3. We derive the BPS equations and find the massless spectrum for both abelian and non-abelian gauge groups in 4d. The mathematical tool that allows us to determine the spectrum is Morse theory, and more generally Morse-Bott theory. We make contact with twisted connected sum (TCS) G2- manifolds, which form the largest class of examples of compact G2-manifolds. M-theory on TCS G2-manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of G2-manifolds and provide a prescription for how to engineer singular transitions to models with chiral matter.</p>
<p>In the second part, we consider GK geometries that arise in AdS compactifications of IIB string theory and M-theory and play a key role in the geometric dual to c-extremization. We provide a mathematically oriented exposition of GK geometries in general dimension. We study the extension of the geometric dual of c-extremization for 2d (0, 2) superconformal field theories (SCFTs) that have an AdS3 dual realized in Type IIB with varying axio-dilaton, i.e. F- theory. M/F-duality implies that such AdS3 solutions can be mapped to AdS2 solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic c-extremization in F- theory and I-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.</p> |
| first_indexed | 2024-03-06T21:24:49Z |
| format | Thesis |
| id | oxford-uuid:42bb8995-0c39-41be-b6de-e12c80746e88 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:45:39Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | oxford-uuid:42bb8995-0c39-41be-b6de-e12c80746e882024-12-07T17:30:43ZSupersymmetric geometries in string theoryThesishttp://purl.org/coar/resource_type/c_db06uuid:42bb8995-0c39-41be-b6de-e12c80746e88Differential geometryString modelsEnglishHyrax Deposit2021Cizel, SSchafer-Nameki, SSparks, J<p>Supersymmetric vacua of string theory endow the internal space with a special geometric structure. We refer to these structures collectively as supersymmetric geometries. The objective of this thesis is to study two classes of supersymmetric geometries and their associated quantum field theories arising from string compactifications.</p> <p>In the first part of this thesis, we study M-theory compactifications on G2- manifolds. We focus on the gauge sector of such compactifications by studying the Higgs bundle, characterizing a local ALE-fibration over a supersymmetric three-cycle M3, obtained from a partially twisted 7d super Yang-Mills theory on M3. We derive the BPS equations and find the massless spectrum for both abelian and non-abelian gauge groups in 4d. The mathematical tool that allows us to determine the spectrum is Morse theory, and more generally Morse-Bott theory. We make contact with twisted connected sum (TCS) G2- manifolds, which form the largest class of examples of compact G2-manifolds. M-theory on TCS G2-manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of G2-manifolds and provide a prescription for how to engineer singular transitions to models with chiral matter.</p> <p>In the second part, we consider GK geometries that arise in AdS compactifications of IIB string theory and M-theory and play a key role in the geometric dual to c-extremization. We provide a mathematically oriented exposition of GK geometries in general dimension. We study the extension of the geometric dual of c-extremization for 2d (0, 2) superconformal field theories (SCFTs) that have an AdS3 dual realized in Type IIB with varying axio-dilaton, i.e. F- theory. M/F-duality implies that such AdS3 solutions can be mapped to AdS2 solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic c-extremization in F- theory and I-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.</p> |
| spellingShingle | Differential geometry String models Cizel, S Supersymmetric geometries in string theory |
| title | Supersymmetric geometries in string theory |
| title_full | Supersymmetric geometries in string theory |
| title_fullStr | Supersymmetric geometries in string theory |
| title_full_unstemmed | Supersymmetric geometries in string theory |
| title_short | Supersymmetric geometries in string theory |
| title_sort | supersymmetric geometries in string theory |
| topic | Differential geometry String models |
| work_keys_str_mv | AT cizels supersymmetricgeometriesinstringtheory |