Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.780786
Title: G-structures and superstrings from the worldsheet
Author: Fiset, Marc-Antoine
ISNI:       0000 0004 7966 4263
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2019
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Abstract:
G-structures, where G is a Lie group, are a uniform characterisation of many differential geometric structures of interest in supersymmetric compactifications of string theories. Calabi-Yau n-folds for instance have torsion-free SU(n)-structure, while more general structures with non-zero torsion are required for heterotic flux compactifications. Exceptional geometries in dimensions 7 and 8 with G = G2 and Spin(7) also feature prominently in this thesis. We discuss multiple connections between such geometries and the world- sheet theory describing strings on them, especially regarding their chiral symmetry algebras, originally due to Odake and Shatashvili-Vafa in the cases where G is SU (n), G2 and Spin(7). In the first part of the thesis, we describe these connections within the formalism of operator algebras. We also realise the superconformal algebra for G2 by combining Odake and free algebras following closely the recent mathematical construction of twisted connected sum G2 manifolds. By considering automorphisms of this realisation, we speculate on mirror symmetry in this context. In the second part of the thesis, G-structures are studied semi-classically from the worldsheet point of view using (1, 0) supersymmetric non-linear σ- models whose target M has reduced structure. Non-trivial flux and instanton- like connections on vector bundles over M are also allowed in order to deal with general applications to superstring compactifications, in particular in the heterotic case. We introduce a generalisation of the so-called special holonomy W-symmetry of Howe and Papadopoulos to σ-models with Fermi and mass sectors. We also investigate potential anomalies and show that cohomologically non-trivial terms in the quantum effective action are invariant under a corrected version of this symmetry. Consistency with supergravity at first order in α' 0 is manifest and discussed. We finally relate marginal deformations of (1, 0) G 2 and Spin(7) σ-models with the cohomology of worldsheet BRST operators. We work at lowest order in α' 0 and study general heterotic backgrounds with bundle and non-vanishing torsion.
Supervisor: Ossa, Xenia de la Sponsor: FRQNT Quebec ; Reidler Scholarship
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.780786  DOI: Not available
Keywords: Geometry ; String models
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