Holography in Field Theory  

In General > s.a. boundaries; duality in field theory; Holographic Screen; physics [visions].
* Idea: The holographic principle is an idea proposed by 't Hooft in 1993, according to which (i) The true degrees of freedom inside a region are enumerated on its surface–like a literal interpretation of Plato's cave allegory–, with (ii) An information density ρinfo ≤ 1 bit /lP2; It relies on the validity of the holographic entropy bound; The issue is, what is the mechanism behind it?
* Motivation: It provides a more economic description of nature than local quantum field theory, having fewer degrees of freedom.
* Weak, "Kinematic": The entropy inside a region is bounded by the area of its boundary; The number of degrees of freedom inside a volume (including gravity) is bounded by the area of the boundary (screen) enclosing this volume.
* Strong, "Dynamic": The dynamics of a system in a volume is described by a system living on the boundary; The degrees of freedom live on the boundary and describe the physics inside the volume completely.
> Online resources: see Wikipedia page.

Examples, Phenomenology > s.a. AdS-cft correspondence [including dS-cft]; entropy bound and quantum entropy; holography in gravitation and cosmology.
* Development: First hints with black-hole thermodynamics (Hawking's area theorem, and Bekenstein's entropy), and attempts at more general area-based entropy bounds such as

SmatterA / 4G\(\hbar\)c3 ,

which fails in strong-gravity, large-curvature situations, and is replaced by the covariant one; 't Hooft's and Susskind's idea of the world as a hologram, which seemed to be realized in quantum field theory, from examples of theories with AdS-cft correspondence (didn't work in general); Persistent ideas of importance in quantum gravity.
* de Alfaro et al: A correspondence between the generating functional for the Green functions of a Euclidean quantum field theory in D dimensions and the Gibbs average for classical statistical mechanics in D+1 dimensions.
* In M-theory: We are on the boundary, and we can probe the bulk dynamics; In 2+1 dimensions, it is satisfied by open and flat models, not closed ones.
* Experiments: Craig Hogan developed the Holometer, a pair of interferometers at Fermilab with which one might detect "holographic noise" in the form of spacelike correlations between the interferometer signals; 2015, The experiment hasn't seen any evidence, but no general analysis of what types of theories the experiment can and cannot test is available.
@ General references: Ogushi & Sasaki PTP(05)ht/04 [in Einstein-Gauss-Bonnet gravity]; Midodashvili ht/06 [in higher dimensions]; Wolf et al PRL(08) [for lattice model in thermal equilibrium]; Dvali et al PRD(16)-a1511 [Stückelberg formulation]; Jokela & Pönni a2007 [statistical approach].
@ Condensed-matter physics: Mefford & Horowitz PRD(14)-a1406 [holographic insulator]; Zaanen et al 16; > s.a. gauge-gravity duality.
@ Fermilab Holometer: news NBC(14)aug; Chou et al PRL(16)-a1512 + Hossenfelder blog(15)dec + news sci(15)dec [results]; Chou et al CQG+(17); Hogan & Kwon CQG(18)-a1711 [exotic cross-correlations and emergent spacetime].
> Related topics: see complexity; composite models; condensed matter; knot invariants; phase transitions; QCD.

References > s.a. cosmological constant; Large-Number Hypothesis; quantum gravity; renormalization group.
@ Reviews: Bigatti & Susskind ht/00-ln; Smolin NPB(01)ht/00; 't Hooft ht/00; Bousso RMP(02)ht; Bekenstein SA(03)aug; Banks IJMPA(10)-a1004-conf [and phenomenology – cosmological constant and supersymmetry]; article vox(15)jun; Luminet IRS-a1602 [critical review]; Baggioli a1908-ln.
@ General references: 't Hooft in(88), gq/93-in; Susskind JMP(95)ht/94; Corley & Jacobson PRD(96)gq; Dawid PLB(99)gq/98; Schroer ht/01; Arcioni et al ht/06-fs [discussions with 't Hooft]; Kay & Larkin PRD(08)-a0708; Osborne et al PRL(10)-a1005; Krishnan a1011-ln [quantum field theory and black-hole physics]; Marolf CQG(14)-a1308 [without strings]; blog sn(14)sep; McInnes & Ong NPB(15)-a1504 [consistency conditions]; Zapata a1704-GRF [and gauge]; Xiao a1710 [microscopic theory with holographic degrees of freedom]; Donnelly a1806 [reconstructing a single-particle quantum state from the metric at spatial infinity].
@ General spacetimes: Bonelli PLB(99)ht/98; Bousso JHEP(99)ht, CQG(00)ht/99-conf; Tavakol & Ellis PLB(99)ht; Riegler a1609-PhD [2+1 non-AdS spacetimes]; Nomura et al PRD(17)-a1611 [without asymptotic regions].
@ Interpretations: Dance qp/04 [in terms of observations].
@ Counterexamples, alternatives: Pinzul & Stern JHEP(01)ht [non-commutative Chern-Simons]; Botta Cantcheff & Nogales IJMPA(06)gq/05 [statistics].
@ Related topics: Álvarez & Gómez NPB(99)ht/98, ht/98-fs [renormalization group, c-theorem]; Minic PLB(98)ht [and uncertainty]; Dzhunushaliev IJMPD(00)gq/99 [event horizons]; Ivanov & Volovich Ent(01)gq/99 [entropy bound]; Bose & Mazumdar gq/99 [quantum]; van de Bruck gq/00 [and stochastic quantization]; Zois RPMP(05)ht/03 [and Deligne conjecture]; Bousso JHEP(04)ht [and quantum mechanics]; Hubeny et al JHEP(05)ht [and causal structure]; Miao a2009 [codimension-2 holography].

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