Holography in Field Theory| 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
Smatter ≤ A / 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].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 28 may 2021