Harmonic forms on asymptotically ADS metrics

Hyper - Kähler Calabi Metrics , L 2 Harmonic Forms , Resolved M 2 - branes , and AdS 4 / CFT 3 Correspondence

Stability in Asymptotically AdS Spaces

We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the case of three dimensional Einstein manifolds, we completely characterize the presence of these instabilities, and in higher dimensions we provide a partial cla...

Complex manifolds, Kahler metrics, differential and harmonic forms

Definition 1.1 (Complex Manifold). A complex manifold is a manifold with coordinates holomorphic on C rather than C∞ on R. What is the difference betwene holomorphic and C∞? From the PDE point of view, they must satisfy the Cauchy-Riemann equations: f(z) = u+ iv is holomorphic if and only if ∂u ∂x = ∂v ∂y and ∂u ∂y = − ∂v ∂x . The fact that this causes the function f to be analytic(holomorphic)...

On 3-dimensional Asymptotically Harmonic Manifolds

Let (M, g) be a complete, simply connected Riemannian manifold of dimension 3 without conjugate points. We show thatM is a hyperbolic manifold of constant sectional curvature −h 2 4 , provided M is asymptotically harmonic of constant h > 0.

Algebraic Holography in Asymptotically Simple, Asymptotically Ads Spacetimes

I’ll describe a general geometric setup allowing a generalization of Rehren duality to asymptotically anti-de Sitter spacetimes whose classical matter distribution is sufficiently well-behaved to prevent the occurence of singularities in the sense of null geodesic incompleteness. I’ll also comment on the issues involved in the reconstruction of an additive and locally covariant bulk net of obse...