We consider the non-interacting massive Wess-Zumino model in four-dimensional anti-de Sitter space and show that the conformal dimensions of the corresponding boundary fields do not always satisfy the relation expected from superconformal invariance.

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonab...

We study the decay of the unstable D-particle in three-dimensional anti-de Sitter space-time using worldsheet boundary conformal field theory methods. We test the open string completeness conjecture in a background for which the phase space available is only field-theoretic. This could present a serious challenge to the claim. We compute the emission of closed strings in the AdS3× S3× T backgro...

We construct a four dimensional Yang-Mills theory with N = 4 twisted supersymmetry whose classical vacua correspond to four dimensional anti-de Sitter space. The theory utilizes a complex gauge field whose real part is a spin connection which is used to enforce local Lorentz invariance. The imaginary part of the connection can then be interpreted as a vierbein. The topological construction ensu...

We show how to extend the usual black string instability of vacuum or charged black p-branes to the anti-de Sitter background. The string fragments in an analogous fashion to the Λ = 0 case, the main difference being that instead of a periodic array of black holes forming, an accumulation of “mini” black holes occurs towards the AdS horizon. In the case where the AdS space is of finite extent, ...

Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalization of the latter at the same time, e.g., geodesics are not unique and may be singular, the Hausdorff dimension is larger than the manifold topological dimension. There exists a la...

An algebra of functions on q–deformed Anti-de Sitter space AdSD q with star-structure is defined for roots of unity, which is covariant under Uq(so(2,D−1)). The scalar fields have an intrinsic high–energy cutoff, and arise most naturally on products of the quantum AdS space with a classical sphere. Hilbert spaces of scalar fields are constructed.

A class of black hole solutions to Einstein’s equations in d dimensions with a negative cosmological constant is constructed. These solutions have the property that the horizon is a (d− 2)-dimensional manifold of constant curvature, but this curvature may be positive, zero, or negative. Asymptotically, the solutions are locally isometric to anti-de Sitter space. The mass, temperature, and entro...

Three dimensional spacelike warped anti-de Sitter space is studied in the context of Einstein theories of gravity and string theory, where there is no gravitational Chern-Simons term in the action. We propose that it is holographically dual to a two-dimensional conformal field theory with equal left and right moving central charges. Various checks of the central charges are offered, based on th...