Related papers: Puzzles and Paradoxes About Holography
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
Choose a polynomial in three variables with not more than three or four monomials of moderate degree. Take simple coefficients as 1 and -1. Then draw a picture of the solution variety in real three space using a ray-tracing program like…
The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…
This paper has been withdrawn by the author as the conjecture proposed in it is wrong.
The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the…
This paper introduces a new concept of one-dimensional hologram which represents one line image, and a new kind of display structure using it. This one-dimensional hologram is similar to a superpositioned diffraction lattice. And the…
We consider three related topics: (a) Holographic quantum field theories on AdS spaces. (b) Holographic interfaces of flat space QFTs. (c) Wormholes connecting generically different QFTs. We investigate in a concrete example how the related…
The AdS/CFT correspondence is useful primarily when the number of colours, $N_{\textsf{c}}$, characterising the boundary field theory, is "large", and when the mass of the bulk black hole that is usually present is "large" relative to the…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
The "periodic table" of strongly coupled gauge theories remains only sketchily understood. Holography has developed to the point where bottom up constructions can describe the spectrum of individual gauge theories (based on assumptions of…
This note has been written on the occasion of Gerard 't Hooft's 60th birthday celebration. It is not a technical paper but just a collection of discussions that the three authors had with Gerard, mostly in relation with the idea of…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
After a brief reminscence about work with K. Sato 25 years ago on the monopole problem and inflation, a discussion is given of the black hole information paradox. It is argued that, quite generally, it should be anticipated that the states…
We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…
Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a…
The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the…
After more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are…
This is one chapter of the collection of problems in cosmology, in which we assemble the problems, with solutions, that concern one of the most distinctive features of general relativity and cosmology---the horizons. The first part gives an…
We spell two conundrums, one of physical and another of mathematical nature, and explain why one helps to elucidate the other
Holographic duality relates two radically different kinds of theory: one with gravity, one without. The very existence of such an equivalence imposes strong consistency conditions which are, in the nature of the case, hard to satisfy.…