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The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string theoretic interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence.
In physics, string theory is a theory that attempts to merge quantum mechanics with Einstein’s general theory of relativity. The theory puts forth the premise of the material universe being made of tiny one-dimensional “strings”, rather than the more conventional approach in which they are modeled as zero-dimensional point particles. String theory envisions that a string undergoing a particular mode of vibration corresponds to a particle with definite properties such as mass and charge.
Duality may refer to:
In mathematical physics, the Wightman axioms, named after Arthur Wightman, are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s, but they were first published only in 1964 after Haag–Ruelle scattering theory affirmed their significance.
Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by Rudolf Haag and Daniel Kastler (1964). The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those.
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.
In gauge theory and mathematical physics, a topological quantum field theory is a quantum field theory which computes topological invariants.
In theoretical physics, the anti-de Sitter/conformal field theory correspondence is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles.
Erik Peter Verlinde is a Dutch theoretical physicist and string theorist. He is the identical twin brother of physicist Herman Verlinde. The Verlinde formula, which is important in conformal field theory and topological field theory, is named after him. His research deals with string theory, gravity, black holes and cosmology. Currently, he works at the Institute for Theoretical Physics at the University of Amsterdam.
Karl-Henning Rehren is a German physicist who focuses on algebraic quantum field theory.
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial perspective.
The non-critical string theory describes the relativistic string without enforcing the critical dimension. Although this allows the construction of a string theory in 4 spacetime dimensions, such a theory usually does not describe a Lorentz invariant background. However, there are recent developments which make possible Lorentz invariant quantization of string theory in 4-dimensional Minkowski space-time.
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics.
In strong interaction physics, light front holography or light front holographic QCD is an approximate version of the theory of quantum chromodynamics (QCD) which results from mapping the gauge theory of QCD to a higher-dimensional anti-de Sitter space (AdS) inspired by the AdS/CFT correspondence proposed for string theory. This procedure makes it possible to find analytic solutions in situations where strong coupling occurs, improving predictions of the masses of hadrons and their internal structure revealed by high-energy accelerator experiments. The most widely used approach to finding approximate solutions to the QCD equations, lattice QCD, has had many successful applications; however, it is a numerical approach formulated in Euclidean space rather than physical Minkowski space-time.
The Bousso bound captures a fundamental relation between quantum information and the geometry of space and time. It appears to be an imprint of a unified theory that combines quantum mechanics with Einstein's general relativity. The study of black hole thermodynamics and the information paradox led to the idea of the holographic principle: the entropy of matter and radiation in a spatial region cannot exceed the Bekenstein–Hawking entropy of the boundary of the region, which is proportional to the boundary area. However, this "spacelike" entropy bound fails in cosmology; for example, it does not hold true in our universe.
This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.
João Miguel Augusto Penedones Fernandes is a Portuguese theoretical physicist active in the area of quantum field theory. He is currently a tenure track assistant professor at the École Polytechnique Fédérale de Lausanne (EPFL).
The Ryu–Takayanagi conjecture is a conjecture within holography that posits a quantitative relationship between the entanglement entropy of a conformal field theory and the geometry of an associated anti-de Sitter spacetime. The formula characterizes "holographic screens" in the bulk; that is, it specifies which regions of the bulk geometry are "responsible to particular information in the dual CFT". The conjecture is named after Shinsei Ryu and Tadashi Takayanagi, who jointly published the result in 2006. As a result, the authors were awarded the 2015 New Horizons in Physics Prize for "fundamental ideas about entropy in quantum field theory and quantum gravity". The formula was generalized to a covariant form in 2007.
Higher-spin theory or higher-spin gravity is a common name for field theories that contain massless fields of spin greater than two. Usually, the spectrum of such theories contains the graviton as a massless spin-two field, which explains the second name. Massless fields are gauge fields and the theories should be (almost) completely fixed by these higher-spin symmetries. Higher-spin theories are supposed to be consistent quantum theories and, for this reason, to give examples of quantum gravity. Most of the interest in the topic is due to the AdS/CFT correspondence where there is a number of conjectures relating higher-spin theories to weakly coupled conformal field theories. It is important to note that only certain parts of these theories are known at present and not many examples have been worked out in detail except some specific toy models.
In quantum gravity and quantum complexity theory, the complexity equals action duality (CA-duality) is the conjecture that the gravitational action of any semiclassical state with an asymptotically anti-de Sitter background corresponds to quantum computational complexity, and that black holes produce complexity at the fastest possible rate. In technical terms, the complexity of a quantum state on a spacelike slice of the conformal field theory dual is proportional to the action of the Wheeler–DeWitt patch of that spacelike slice in the bulk. The WDW patch is the union of all possible spacelike slices of the bulk with the CFT slice as its boundary.
References
- Rehren, K.-H. (2000). "Algebraic Holography". Annales Henri Poincaré. 1 (4): 607–623. arXiv: hep-th/9905179 . Bibcode:2000AnHP....1..607R. doi:10.1007/pl00001009. ISSN 1424-0637. S2CID 5966399.
For a classical counterpart to Rehren duality see
- Kay, Bernard S.; Larkin, Peter (18 June 2008). "Pre-holography". Physical Review D. 77 (12): 121501(R). arXiv: 0708.1283 . Bibcode:2008PhRvD..77l1501K. doi:10.1103/physrevd.77.121501. ISSN 1550-7998. S2CID 263787154.