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
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].

> __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].

@ __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 2 aug 2017