Related papers: Puzzles and Paradoxes About Holography
Holographic screens are codimension-one hypersurfaces that extend the notion of apparent horizons to general (non-black hole) spacetimes and that display interesting thermodynamic properties. We show that if a spacetime contains a…
Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
This is an innovative treatise on triangles, resting upon 1) 3-body problem techniques including mass-weighted relative Jacobi coordinates. 2) Part I's detailed layer-by-layer topological and geometrical study of Kendall-type shape spaces -…
The holographic principle is tested by examining the logarithmic and higher order corrections to the Bekenstein-Hawking entropy of black holes. For the BTZ black hole, I find some disagreement in the principle for a holography screen at…
We continue our discussion from part I.
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
This paper explores the enduring black hole information and firewall paradoxes, challenges that have prompted many proposals, conjectures, and theories. Noteworthy among these are the ER = EPR conjecture and AdS/CFT correspondence, which…
Discrete geometries in hyperbolic space are of longstanding interest in pure mathematics and have come to recent attention in holography, quantum information, and condensed matter physics. Working at a purely geometric level, we describe…
This is a brief, popular-level introduction to holographic entanglement. It was published in the newsletter of the International Centre for Theoretical Sciences, Bangalore.
An edge tessellation is a tiling of the plane generated by reflecting a polygon in its edges. We prove that a polygon generating an edge tessellation is one the following eight types: a rectangle; an equilateral, 60-right, isosceles right,…
After a pedagogical overview of the present status of High-Energy Physics, some problems concerning physics at the Planck scale are formulated, and an introduction is given to a notion that became known as ``the holographic principle" in…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E.
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obvious constraints), there exists a geometric…
In this work we review at an elementary level the origin, main ideas and present status of the so called holographic principle. This principle, even in the absence of a precise formulation, is seen by many people as a major clue for the…
Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…
We decompose sphere partition functions and indices of three-dimensional N=2 gauge theories into a sum of products involving a universal set of "holomorphic blocks". The blocks count BPS states and are in one-to-one correspondence with the…