134 research outputs found
Generalised -structures and type IIB superstrings
The recent mathematical literature introduces generalised geometries which
are defined by a reduction from the structure group of the vector
bundle to a special subgroup. In this article we show that
compactification of IIB superstring vacua on 7-manifolds with two covariantly
constant spinors leads to a generalised -structure associated with a
reduction from SO(7,7) to . We also consider compactifications
on 6-manifolds where analogously we obtain a generalised SU(3)-structure
associated with , and show how these relate to generalised
-structures.Comment: 14 pages, v2: Section 4 rewritten and references added, final version
of the paper to appear in JHE
A heat flow for special metrics
On the space of positive 3-forms on a seven-manifold, we study a natural
functional whose critical points induce metrics with holonomy contained in
. We prove short-time existence and uniqueness for its negative gradient
flow. Furthermore, we show that the flow exists for all times and converges
modulo diffeomorphisms to some critical point for any initial condition
sufficiently -close to a critical point.Comment: 35 pages, slightly revise
Special metric structures and closed forms
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 . As
such, the forms we consider induce a reduction from to . We give a topological classification of -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.Comment: examined DPhil Thesis, University of Oxford, 2004 v2: Proposition 3.5
and Theorem 3.6 fixe
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