Special metric structures and closed forms

Abstract

The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3) acting in its adjoint representation. We derive various obstructions to the existence of a topological reduction to PSU(3). For compact manifolds, we also find sufficient conditions if the PSU(3)-structure lifts to an SU(3)-structure. We give a Riemannian characterisation of topological PSU(3)-structures through an invariant spinor valued 1-form and show that the PSU(3)-structure is integrable if and only if the spinor valued 1-form defines a co-closed Rarita-Schwinger field. Moreover, we construct non-symmetric (compact) examples. Secondly, we consider even or odd forms which can be naturally interpreted as spinors for a spin structure on $T\oplus T^{\ast }$. As such, the forms we consider induce a reduction from $Spin(7,7)$ to $G_2\times G_2$. We give a topological classification of $G_2\times G_2$-structures. We prove that the condition for being a critical point is equivalent to the supersymmetry equations on spinors in supergravity theory of type IIA/B with NS-NS background fields. Examples are systematically constructed by the device of T-duality.

examined DPhil Thesis, University of Oxford, 2004 v2: Proposition 3.5 and Theorem 3.6 fixed

References in corpus (8)

• New Supersymmetric String Compactifications
• Superstrings with Intrinsic Torsion
• G-Structures and Wrapped NS5-Branes
• Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds
• New aspects of the ddc-lemma
• Kaehler reduction of metrics with holonomy G_2
• G_2-structures with torsion from half-integrable nilmanifolds
• Almost Parallel Structures

Cited by in corpus (26)

• Generalized structures of N=1 vacua
• A scan for new N=1 vacua on twisted tori
• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• Twisted differential String and Fivebrane structures
• Generalised $G_2$-structures and type IIB superstrings
• Leibniz algebroids, twistings and exceptional generalized geometry
• New aspects of the ddc-lemma
• Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry
• Closed forms and multi-moment maps
• Calibrated cycles and T-duality
• N=1 domain wall solutions of massive type II supergravity as generalized geometries
• Spin(7)-manifolds in compactifications to four dimensions
• The Topological G2 String
• Obstruction theory on 8-manifolds
• Special metrics and Triality
• M-theory, the signature theorem, and geometric invariants
• Fermions, differential forms and doubled geometry
• Manifolds admitting stable forms
• Flux Backgrounds and Exceptional Generalised Geometry
• Manifolds admitting a ${\tilde{G}}_2$-structure
• Singular foliations for M-theory compactification
• Product twistor spaces and Weyl geometry
• Reduction of metric structures on Courant algebroids
• The complex world of superstrings: On semichiral sigma models