holographic principle

holographic principle
Name	Holographic principle
Caption	Conceptual depiction of information encoded on a boundary surface
Field	Theoretical physics
Introduced	1990s
Proponents	Gerard 't Hooft; Leonard Susskind; Juan Maldacena
Related	Black hole thermodynamics; AdS/CFT correspondence; string theory

holographic principle The holographic principle is a conjectured relationship between theories of gravity in a volume and non-gravitational theories on the boundary of that volume. It emerged from attempts to reconcile Stephen Hawking's results on Hawking radiation and Jacob Bekenstein's work on Bekenstein–Hawking entropy with ideas in Gerard 't Hooft's and Leonard Susskind's formulations and was crystallized by Juan Maldacena's AdS/CFT correspondence proposal. The principle has influenced research programs in string theory, quantum gravity, and studies of black hole information paradox.

Overview

The holographic principle proposes that the maximal entropy or information content of a spatial region scales with the area of its boundary, not the volume, linking ideas from Bekenstein bound and Bekenstein–Hawking entropy. It suggests dualities between bulk gravitational descriptions such as those in anti-de Sitter space and boundary quantum field theories exemplified by conformal field theory. Prominent formulations connect M-theory, Type IIB string theory, and low-energy limits of supergravity to lower-dimensional non-gravitational models.

Historical development

Origins trace to Jacob Bekenstein's 1970s proposal of an entropy bound inspired by thought experiments with black hole thermodynamics and the discovery of Hawking radiation by Stephen Hawking. In the early 1990s Gerard 't Hooft articulated a first explicit statement of holographic scaling while Leonard Susskind developed complementary arguments invoking black hole complementarity and participated in debates with John Preskill over the black hole information paradox. The late 1990s saw a major development when Juan Maldacena proposed the AdS/CFT correspondence, bringing rigorous examples that realized holographic duality within string theory and linking to results by Edward Witten, Steven Gubser, Mikhail R. Douglas, and Cumrun Vafa.

Theoretical foundations

Foundations rest on combining semiclassical results from Stephen Hawking and Jacob Bekenstein with quantum field theoretic and string theoretic methods developed by groups at Princeton University, Institute for Advanced Study, Harvard University, and CERN. Theoretical tools include conformal field theory techniques used by Alexander Polyakov and Alexander Zamolodchikov, path integral methods of Richard Feynman adapted in Edward Witten's work, and dualities within M-theory and Type IIB string theory explored by Michael Green, John Schwarz, and Paul Townsend. Key mathematical structures invoked are the Anti-de Sitter space geometry, conformal symmetry, and entropy bounds derived from semiclassical analyses by Don Page and Bill Unruh. Concepts such as entanglement entropy studied by Mark Srednicki and Calabrese-Cardy techniques provide microscopic interpretations of boundary degrees of freedom tied to bulk geometry in holographic setups.

Applications and implications

Holography has been applied across topics pursued at Institute for Advanced Study and Perimeter Institute, influencing models in condensed matter physics via AdS/CMT analogies used by researchers like Subir Sachdev and Sean Hartnoll. It has informed approaches to the black hole information paradox debated by Don Page and Joseph Polchinski, inspired proposals for firewall scenarios tied to work by Almheiri-Marolf-Polchinski-Sully authors, and guided quantum cosmology efforts involving Inflationary cosmology questions considered by Alan Guth and Andrei Linde. Holographic methods have been used to model quark–gluon plasma phenomena studied at Relativistic Heavy Ion Collider and Large Hadron Collider through collaborations influenced by Maldacena's conjecture, and to explore computational complexity conjectures advanced by Leonard Susskind and Brian Swingle.

Evidence and tests

Direct experimental tests remain limited; holography is supported by a body of theoretical checks exemplified by matches of correlation functions computed in AdS/CFT correspondence by Edward Witten and Gubser-Klebanov-Polyakov with expectations from N = 4 supersymmetric Yang–Mills theory studied by Nathan Seiberg and Edward Witten. Precision checks include comparisons of thermal entropy and transport coefficients between gravitational black brane solutions explored by Dam Thanh Son and Andrei Starinets and strongly coupled plasma data from RHIC and ALICE. Numerical holography work by groups at Perimeter Institute and Stanford University uses lattice techniques and tensor network proposals connected to Brian Swingle and Guifre Vidal to probe entanglement structure consistent with holographic scaling.

Criticisms and alternatives

Critics including researchers in approaches like loop quantum gravity (groups around Carlo Rovelli and Lee Smolin) argue the principle may be an artifact of specific asymptotic geometries such as anti-de Sitter space and question extensions to de Sitter space relevant for cosmology pursued by Eva Silverstein and Tom Banks. Alternative frameworks propose different microstate accounting for Bekenstein–Hawking entropy explored by Ashoke Sen in string microstate counting, or rely on canonical quantization strategies developed by Abhay Ashtekar. Debates continue in forums at Perimeter Institute and Simons Foundation workshops concerning the generality, operational meaning, and empirical accessibility of holographic dualities.

Category:Theoretical physics