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 *ρ*_{info}
≤ 1 bit /*l*_{P}^{2}; It
relies on the validity of the holographic entropy bound; The issue is,
what is the mechanism behind it?

* __Motivation__:
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

*S*_{matter} ≤ *A*
/ 4*G*\(\hbar\)*c*^{3} ,

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].

@ __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 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].

@ __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].

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send feedback and suggestions to bombelli at olemiss.edu – modified 13 nov 2018