CA-duality

Last updated

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. [1] 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 (WDW 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. [2] [3] [4]

This conjecture has been tested against several anti-de Sitter black hole backgrounds with and without shock waves, and was found to pass all the tests. [3] The action for the WDW patch of a wormhole grows linearly in time for an exponentially long period. Dually, quantum circuit complexity has also been shown to grow linearly for an exponentially long time [5]

Related Research Articles

The holographic principle is an axiom in 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-theory 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 theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity.

<span class="mw-page-title-main">No-hair theorem</span> Black holes are characterized only by mass, charge, and spin

The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, electric charge, and angular momentum. Other characteristics are uniquely determined by these three parameters, and all other information about the matter that formed a black hole or is falling into it "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers after the black hole "settles down". Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair", which was the origin of the name.

<span class="mw-page-title-main">Black hole thermodynamics</span> Area of study

In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. As the study of the statistical mechanics of black-body radiation led to the development of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.

<span class="mw-page-title-main">Juan Maldacena</span> Argentine physicist (born 1968)

Juan Martín Maldacena is an Argentine theoretical physicist and the Carl P. Feinberg Professor in the School of Natural Sciences at the Institute for Advanced Study, Princeton. He has made significant contributions to the foundations of string theory and quantum gravity. His most famous discovery is the AdS/CFT correspondence, a realization of the holographic principle in string theory.

In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, 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.

<span class="mw-page-title-main">Leonard Susskind</span> American physicist

Leonard Susskind is an American physicist, who is a professor of theoretical physics at Stanford University, and founding director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.

The Unruh effect is a kinematic prediction of quantum field theory that an accelerating observer will observe a thermal bath, like blackbody radiation, whereas an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layman's terms, an accelerating thermometer in empty space, removing any other contribution to its temperature, will record a non-zero temperature, just from its acceleration. Heuristically, for a uniformly accelerating observer, the ground state of an inertial observer is seen as a mixed state in thermodynamic equilibrium with a non-zero temperature bath.

Micro black holes, also called mini black holes or quantum mechanical black holes, are hypothetical tiny black holes, for which quantum mechanical effects play an important role. The concept that black holes may exist that are smaller than stellar mass was introduced in 1971 by Stephen Hawking.

<span class="mw-page-title-main">Quantum field theory in curved spacetime</span> Extension of quantum field theory to curved spacetime

In theoretical physics, quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory treats spacetime as a fixed, classical background, while giving a quantum-mechanical description of the matter and energy propagating through that spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. The most famous example of the latter is the phenomenon of Hawking radiation emitted by black holes.

Subir Sachdev is Herchel Smith Professor of Physics at Harvard University specializing in condensed matter. He was elected to the U.S. National Academy of Sciences in 2014, and received the Lars Onsager Prize from the American Physical Society and the Dirac Medal from the ICTP in 2018. He was a co-editor of the Annual Review of Condensed Matter Physics from 2017-2019.

Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Larus Thorlacius, and Gerard 't Hooft.

A causal patch is a region of spacetime connected within the relativistic framework of causality.

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.

Raphael Bousso is a theoretical physicist and cosmologist. He is a professor at the Berkeley Center for Theoretical Physics in the Department of Physics, UC Berkeley. He is known for the Bousso bound on the information content of the universe. With Joseph Polchinski, Bousso proposed the string theory landscape as a solution to the cosmological constant problem.

The FRW/CFT duality is a conjectured duality for Friedmann–Robertson–Walker models inspired by the AdS/CFT correspondence. It assumes that the cosmological constant is exactly zero, which is only the case for models with exact unbroken supersymmetry. Because the energy density does not approach zero as we approach spatial infinity, the metric is not asymptotically flat. This is not an asymptotically cold solution.

A black hole firewall is a hypothetical phenomenon where an observer falling into a black hole encounters high-energy quanta at the event horizon. The "firewall" phenomenon was proposed in 2012 by physicists Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully as a possible solution to an apparent inconsistency in black hole complementarity. The proposal is sometimes referred to as the AMPS firewall, an initialism for the names of the authors of the 2012 paper. The potential inconsistency pointed out by AMPS had been pointed out earlier by Samir Mathur who used the argument in favour of the fuzzball proposal. The use of a firewall to resolve this inconsistency remains controversial, with physicists divided as to the solution to the paradox.

ER = EPR is a conjecture in physics stating that two entangled particles are connected by a wormhole and is thought by some to be a basis for unifying general relativity and quantum mechanics into a theory of everything.

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.

Douglas Stanford is an American theoretical physicist. He is an associate professor of physics at Stanford Institute for Theoretical Physics of Stanford University. His research interests include quantum gravity, quantum field theory and string theory. Stanford was awarded the 2018 New Horizons in Physics Prize by Fundamental Physics Prize Foundation for his work on improving the understanding of quantum mechanics of black holes via chaos theory.

References

  1. Hartman, Thomas (9 May 2016). "Black Holes Produce Complexity Fastest". Physics. 9: 49. doi: 10.1103/Physics.9.49 .
  2. Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard; Swingle, Brian; Zhao, Ying (2016-05-09). "Complexity Equals Action". Physical Review Letters. 116 (19): 191301. arXiv: 1509.07876 . doi:10.1103/PhysRevLett.116.191301. ISSN   0031-9007. PMID   27232013.
  3. 1 2 Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard; Swingle, Brian; Zhao, Ying (2016-04-18). "Complexity, action, and black holes". Physical Review D. 93 (8): 086006. arXiv: 1512.04993 . doi:10.1103/PhysRevD.93.086006. ISSN   2470-0010. S2CID   55031668.
  4. Carmi, Dean; Myers, Robert C.; Rath, Pratik (March 2017). "Comments on Holographic Complexity". Journal of High Energy Physics. 2017 (3): 118. arXiv: 1612.00433 . doi:10.1007/JHEP03(2017)118. ISSN   1029-8479. S2CID   111385742.
  5. Haferkamp, Jonas; Faist, Philippe; Kothakonda, Naga B. T.; Eisert, Jens; Yunger Halpern, Nicole (2022-03-28). "Linear growth of quantum circuit complexity". Nature Physics. 18 (5): 528–532. doi: 10.1038/s41567-022-01539-6 . ISSN   1745-2481. S2CID   235390872.