Some comments on embedding inflation in the AdS/CFT correspondence

The anti-de Sitter space/conformal field theory correspondence (AdS/CFT) can potentially provide a complete formulation of string theory on a landscape of stable and metastable vacua that naturally give rise to eternal inflation. As a model for this process, we consider bubble solutions with de Sitter interiors, obtained by patching together dS and Schwarzschild-AdS solutions along a bubble wall. For an interesting subclass of these solutions the bubble wall reaches spacelike infinity in the black hole interior. Including the effects of perturbations leads to a null singularity emanating from this point. Such solutions are interpreted as states in a single CFT, and are shown to be compatible with holographic entropy bounds. The construction suggests de Sitter entropy be interpreted as the total number of degrees of freedom in effective field theory, with a novel adaptive stepsize cutoff.Comment: 15 pages, 4 figures, revtex

Feed-forward neural networks and topographic mappings for exploratory data analysis

A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling

Initial states and infrared physics in locally de Sitter spacetime

The long wavelength physics in a de Sitter region depends on the initial quantum state. While such long wavelength physics is under control for massive fields near the Hartle-Hawking vacuum state, such initial states make unnatural assumptions about initial data outside the region of causal contact of a local observer. We argue that a reasonable approximation to a maximum entropy state, one that makes minimal assumptions outside an observer's horizon volume, is one where a cutoff is placed on a surface bounded by timelike geodesics, just outside the horizon. For sufficiently early times, such a cutoff induces secular logarithmic divergences with the expansion of the region. For massive fields, these effects sum to finite corrections at sufficiently late times. The difference between the cutoff correlators and Hartle-Hawking correlators provides a measure of the theoretical uncertainty due to lack of knowledge of the initial state in causally disconnected regions. These differences are negligible for primordial inflation, but can become significant during epochs with very long-lived de Sitter regions, such as we may be entering now.Comment: 19 pages, 4 figures, references adde

Holographic representation of local bulk operators

The Lorentzian AdS/CFT correspondence implies a map between local operators in supergravity and non-local operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates the holographic bound.Comment: 36 pages, LaTeX, 4 eps figure

Comments on the black hole information problem

String theory provides numerous examples of duality between gravitational theories and unitary gauge theories. To resolve the black hole information paradox in this setting, it is necessary to better understand how unitarity is implemented on the gravity side. We argue that unitarity is restored by nonlocal effects whose initial magnitude is suppressed by the exponential of the Bekenstein-Hawking entropy. Time-slicings for which effective field theory is valid are obtained by demanding the mutual back-reaction of quanta be small. The resulting bounds imply that nonlocal effects do not lead to observable violations of causality or conflict with the equivalence principle for infalling observers, yet implement information retrieval for observers who stay outside the black hole.Comment: 18 pages, 2 figures, revtex, v2 figure added and some improvements to presentatio

What Is a Thing?

‘Thing’ in the titular question should be construed as having the utmost generality. In the relevant sense, a thing just is an entity, an existent, a being. The present task is to say what a thing of any category is. This task is, I believe, the primary one of any comprehensive and systematic metaphysics. Indeed, an answer provides the means for resolving perennial disputes concerning the integrity of the structure in reality—whether some of the relations among things are necessary merely given those relata themselves—and the intricacy of this structure—whether some things are more or less fundamental than others. After considering some reasons for thinking the generality of the titular question makes it unanswerable, I propound the methodology, original inquiry, required to answer it. The key to this methodology is adopting a singular perspective; confronting the world as merely the impetus to inquiry, one can attain an account of what a thing must be. Radical ontology is a systematic metaphysics—broadly Aristotelian, essentialist and nonhierarchical—that develops the consequences of this account. With it, it is possible to move past stalemate in metaphysics by revealing the grounds of a principled choice between seemingly incommensurable worldviews

Constructing local bulk observables in interacting AdS/CFT

Local operators in the bulk of AdS can be represented as smeared operators in the dual CFT. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-N factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.Comment: 41 pages, LaTeX. v2: reference correcte

Catalog of the Scorpions of the World (1758-1998)

This unique and timely publication is the first such Catalog to be produced in over 100 years. The last full survey of the taxonomy of the world fauna of the Order Scorpiones was by Karl Kraepelin in 1899 - Scorpiones und Pedipalpi. Das Tierreich. Herausgegeben von der Deutschen Zoologischen Gesellschaft. Berlin. Since then, the sheer number of known species and subspecies has increased more than fourfold, and the classification of scorpions has been greatly transformed at both the generic and familial levels. This new Catalog brings together under one cover an enormous amount of difficult-to-locate information on scorpion nomenclature, biogeography, distribution and phylogeny, published before and after Kraepelin\u27s time. It is of special interest because of the unique status that scorpions currently enjoy as models for the study of evolutionary biology, ecology, toxicology, and physiology

Statistical Entropy of Nonextremal Four-Dimensional Black Holes and U-Duality

We identify the states in string theory which are responsible for the entropy of near-extremal rotating four-dimensional black holes in $N=8$ supergravity. For black holes far from extremality (with no rotation), the Bekenstein-Hawking entropy is exactly matched by a mysterious duality invariant extension of the formulas derived for near-extremal black holes states.Comment: 9 pages, harvma