The AdS/CFT Correspondence Conjecture and Topological Censorship

In gr-qc/9902061 it was shown that (n+1)-dimensional asymptotically anti-de-Sitter spacetimes obeying natural causality conditions exhibit topological censorship. We use this fact in this paper to derive in arbitrary dimension relations between the topology of the timelike boundary-at-infinity, \scri, and that of the spacetime interior to this boundary. We prove as a simple corollary of topological censorship that any asymptotically anti-de Sitter spacetime with a disconnected boundary-at-infinity necessarily contains black hole horizons which screen the boundary components from each other. This corollary may be viewed as a Lorentzian analog of the Witten and Yau result hep-th/9910245, but is independent of the scalar curvature of \scri. Furthermore, the topology of V', the Cauchy surface (as defined for asymptotically anti-de Sitter spacetime with boundary-at-infinity) for regions exterior to event horizons, is constrained by that of \scri. In this paper, we prove a generalization of the homology results in gr-qc/9902061 in arbitrary dimension, that H_{n-1}(V;Z)=Z^k where V is the closure of V' and k is the number of boundaries $\Sigma_i$ interior to $\Sigma_0$. As a consequence, V does not contain any wormholes or other compact, non-simply connected topological structures. Finally, for the case of n=2, we show that these constraints and the onto homomorphism of the fundamental groups from which they follow are sufficient to limit the topology of interior of V to either B^2 or $I\times S^1$.Comment: Revtex, 20 page

Improved tensor-product expansions for the two-particle density matrix

We present a new density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming Hartree-Fock at metallic valence electron densities. For isolated atoms and ions, it is on a par with previous density-matrix functionals and generalized gradient approximations to density-functional theory. We also present analytic results for the correlation energy in the low density limit of the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure

Comments on the Boundary Scattering Phase

We present a simple solution to the crossing equation for an open string worldsheet reflection matrix, with boundaries preserving a SU(1|2)^2 residual symmetry, which constrains the boundary dressing factor. In addition, we also propose an analogous crossing equation for the dressing factor where extra boundary degrees of freedom preserve a SU(2|2)^2 residual symmetry.Comment: 14 pages, 2 figures; v2: affiliation correcte

Spectropolarimetry of the Deep Impact target comet 9P/Tempel 1 with HiVIS

High resolution spectropolarimetry of the Deep Impact target, comet 9P/ Tempel 1, was performed during the impact event on July 4th, 2005 with the HiVIS Spectropolarimeter and the AEOS 3.67m telescope on Haleakala, Maui. We observed atypical polarization spectra that changed significantly in the few hours after the impact. The polarization of scattered light as a function of wavelength is very sensitive to the size and composition (complex refractive index) of the scattering particles as well as the scattering geometry. As opposed to most observations of cometary dust, which show an increase in the linear polarization with the wavelength (at least in the visible domain and for phase angles greater than about 30%, a red polarization spectrum) observations of 9P/Tempel 1 at a phase angle of 41 degrees beginning 8 minutes after impact and centered at 6:30UT showed a polarization of 4% at 650 nm falling to 3% at 950 nm. The next observation, centered an hour later showed a polarization of 7% at 650 nm falling to 2% at 950nm. This corresponds to a spectropolarimetric gradient, or slope, of -0.9% per 1000 Angstroms 40 minutes after impact, decreasing to a slope of -2.3% per 1000 Angstroms an hour and a half after impact. This is an atypical blue polarization slope, which became more blue 1 hour after impact. The polarization values of 4% and 7% at 650nm are typical for comets at this scattering angle, whereas the low polarization of 2% and 3% at 950nm is not. We compare observations of comet 9P/Tempel 1 to that of a typical comet, C/2004 Machholz, at a phase angle of 30 degrees which showed a typical red slope, rising from 2% at 650nm to 3% at 950nm in two different observations (+1.0 and +0.9% per 1000 Angstroms).Comment: Icarus Deep Impact special issue, accepted Aug 28 200

The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons

We extend the Zamolodchikov-Faddeev algebra for the superstring sigma model on $AdS_{5}\times S^{5}$, which was formulated by Arutyunov, Frolov and Zamaklar, to the case of open strings attached to maximal giant gravitons, which was recently considered by Hofman and Maldacena. We obtain boundary $S$-matrices which satisfy the standard boundary Yang-Baxter equation.Comment: 22 pages, no figure; added a referenc

Quantum Locality

It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is no reason to suspect any conflict between quantum theory and special relativity.Comment: Introduction has been revised, references added, minor corrections elsewhere. To appear in Foundations of Physic

The extremal limits of the C-metric: Nariai, Bertotti-Robinson and anti-Nariai C-metrics

In two previous papers we have analyzed the C-metric in a background with a cosmological constant, namely the de Sitter (dS) C-metric, and the anti-de Sitter (AdS) C-metric, following the work of Kinnersley and Walker for the flat C-metric. These exact solutions describe a pair of accelerated black holes in the flat or cosmological constant background, with the acceleration A being provided by a strut in-between that pushes away the two black holes. In this paper we analyze the extremal limits of the C-metric in a background with generic cosmological constant. We follow a procedure first introduced by Ginsparg and Perry in which the Nariai solution, a spacetime which is the direct topological product of the 2-dimensional dS and a 2-sphere, is generated from the four-dimensional dS-Schwarzschild solution by taking an appropriate limit, where the black hole event horizon approaches the cosmological horizon. Similarly, one can generate the Bertotti-Robinson metric from the Reissner-Nordstrom metric by taking the limit of the Cauchy horizon going into the event horizon of the black hole, as well as the anti-Nariai by taking an appropriate solution and limit. Using these methods we generate the C-metric counterparts of the Nariai, Bertotti-Robinson and anti-Nariai solutions, among others. One expects that the solutions found in this paper are unstable and decay into a slightly non-extreme black hole pair accelerated by a strut or by strings. Moreover, the Euclidean version of these solutions mediate the quantum process of black hole pair creation, that accompanies the decay of the dS and AdS spaces

Quantifying Entanglement Production of Quantum Operations

The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic. A particular case is the entanglement produced by a density operator or a density matrix. The suggested measure is valid for operations over pure states as well as over mixed states, for equilibrium as well as nonequilibrium processes. Systems of arbitrary nature can be treated, described either by field operators, spin operators, or any other kind of operators, which is realized by constructing generalized density matrices. The interplay between entanglement production and phase transitions in statistical systems is analysed by the examples of Bose-Einstein condensation, superconducting transition, and magnetic transitions. The relation between the measure of entanglement production and order indices is analysed.Comment: 20 pages, Revte

Pair creation of anti-de Sitter black holes on a cosmic string background

We analyze the quantum process in which a cosmic string breaks in an anti-de Sitter (AdS) background, and a pair of charged or neutral black holes is produced at the ends of the strings. The energy to materialize and accelerate the pair comes from the strings tension. In an AdS background this is the only study done in the process of production of a pair of correlated black holes with spherical topology. The acceleration $A$ of the produced black holes is necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant. Only in this case the virtual pair of black holes can overcome the attractive background AdS potential well and become real. The instantons that describe this process are constructed through the analytical continuation of the AdS C-metric. Then, we explicitly compute the pair creation rate of the process, and we verify that (as occurs with pair creation in other backgrounds) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of exp(Area/4), where Area is the black hole horizon area. We also conclude that the general behavior of the pair creation rate with the mass and acceleration of the black holes is similar in the AdS, flat and de Sitter cases, and our AdS results reduce to the ones of the flat case when L=0.Comment: 13 pages, 3 figures, ReVTeX

Giant Gravitons - with Strings Attached (III)

We develop techniques to compute the one-loop anomalous dimensions of operators in the ${\cal N}=4$ super Yang-Mills theory that are dual to open strings ending on boundstates of sphere giant gravitons. Our results, which are applicable to excitations involving an arbitrary number of open strings, generalize the single string results of hep-th/0701067. The open strings we consider carry angular momentum on an S$^3$ embedded in the S$^5$ of the AdS$_5\times$S$^5$ background. The problem of computing the one loop anomalous dimensions is replaced with the problem of diagonalizing an interacting Cuntz oscillator Hamiltonian. Our Cuntz oscillator dynamics illustrates how the Chan-Paton factors for open strings propagating on multiple branes can arise dynamically.Comment: 66 pages; v2: improved presentatio