The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group SO(d, d) of the vector bundle T d ⊕ T d * to a special subgroup. In this article we show that compactification of IIB superstring vacua on 7manifolds with two covariantly constant spinors leads to a generalised G 2 -structure associated with a reduction from SO(7, 7) to G 2 ×G 2 . We also consider compactifications on 6-manifolds where analogously we obtain a generalised SU (3)-structure associated with SU (3) × SU (3), and show how these relate to generalised G 2 -structures.
Abstract. We associate to each stable Higgs pair (A0, Φ0) on a compact Riemann surface X a singular limiting configuration (A∞, Φ∞), assuming that det Φ has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions (At, tΦt) to Hitchin's equations which converge to this limiting configuration as t → ∞. This provides a new proof, via gluing methods, for elements in the ends of the Higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space.
We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points generalise the notion of a manifold of holonomy G2, while the constrained ones give rise to a new geometry without a classical counterpart. We characterise these structures by means of spinors and show the integrability conditions to be equivalent to the supersymmetry equations on spinors in type II supergravity theory with bosonic background fields. In particular, this geometry can be described by two linear metric connections with skew-symmetric torsion. Finally, we construct explicit examples by introducing the device of T -duality.Remark: There is a canonical embedding GL + (n) ֒→ Spin(n, n) of the identity component of GL(n) into the spin group of T ⊕ T * . As a GL + (n)-module we have S ± = Λ ev,od T * ⊗ (Λ n T ) 1/2 ,
Abstract. Let M be a compact spin manifold. On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M ≥ 3, are precisely the pairs (g, ϕ) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor ϕ. We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.
We study the asymptotics of the natural L 2 metric on the Hitchin moduli space with group G = SU(2). Our main result, which addresses a detailed conjectural picture made by Gaiotto, Neitzke and Moore [GMN], is that on the regular part of the Hitchin system, this metric is well-approximated by the semiflat metric from [GMN]. We prove that the asymptotic rate of convergence for gauged tangent vectors to the moduli space has a precise polynomial expansion, and hence that the difference between the two sets of metric coefficients in a certain natural coordinate system also has polynomial decay. New work by Dumas and Neitzke shows that the convergence is actually exponential in directions tangent to the Hitchin section.
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