Holography
in Field Theory| Holography
in Field Theory |
In General > s.a. boundaries; physics [visions].
* Idea: 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 
info
1 bit /lP2;
Relies on the validity of the holographic
entropy bound; The issue is, what is the mechanism behind it?
* Motivation: Provides
a more economic descritption 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.
Examples, Realizations > s.a. AdS-cft [including
dS-cft]; composite models [preons]; entropy
bound and quantum
entropy; QCD.
* 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
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.
@ References: Ogushi & Sasaki PTP(05)ht/04 [in
Einstein-Gauss-Bonnet
gravity]; Midodashvili ht/06 [higher
dimensions]; Wolf et al PRL(08) [for lattice model in thermal equilibrium].
Cosmology and Gravitation > s.a. gravitational
action; quantum gravity
phenomenology.
@ General references: Maldacena SA(05)nov; Sotiriou & Liberati PRD(06)gq [field
equations from surface action]; Padmanabhan IJMPD(06)gq-in
from semiclassical action]; Susskind a0710;
Nitti MPLA(08)-a0801 [emergent
4D gravity, rev]; > s.a. ads-cft.
@ Cosmology: Fischler & Susskind ht/98;
Polchinski et al PRD(99)ht;
Easther & Lowe
PRL(99)ht;
Kaloper & Linde
PRD(99)ht;
Bak & Rey CQG(00)ht/99 [strings];
Wang & Abdalla PLB(99)ht,
PLB(00)ht/99 [2+1];
Banks & Fischler
ht/01/JHEP;
Carneiro gq/02;
Vollick ht/03 [closed
universes]; Banks & Fischler ht/03-in
[3.0], ht/04-in;
> s.a. dark energy.
@ Early universe: Myung PLB(04)ht/03 [and
the cosmological constant]; Banks & Fischler
ht/04-GRF
[dense
black hole fluid].
@ Inflation: Danielsson JCAP(03)ht;
Lowe & Marolf PRD(04)ht [eternal].
@ Asymptotically flat spacetimes: de Boer & Solodukhin NPB(03)ht,
Solodukhin ht/04 [Minkowski
space];
Arcioni & Dappiaggi
NPB(03)ht,
CQG(04)ht/03;
Dappiaggi et al RVMP(06)gq/05;
Dappiaggi ht/05-in.
@ And quantum gravity / cosmology: Smolin gq/95;
Krasnov PRD(97)gq/96;
Smolin PRD(00)ht/98;
Markopoulou & Smolin
ht/99; Zizzi
Ent(00)gq/99-in;
Biswas et
al PLB(99)
[stringy,
pre-big-bang];
Horava & Minic PRL(00)ht [
=
0]; de Haro ht/01-PhD;
Pfeiffer
PLB(04)gq/03 [triangulated
quantum gravity]; Davis ht/04-wd;
Padmanabhan gq/04-in
[and Einstein-Hilbert action]; Canfora & Vilasi PLB(05)gq [hints
from holography]; Gambini & Pullin IJMPD(08)-a0708
[spherically symmetric lqg].
@ Related topics: Livine & Terno a0805 [entropic boundary law in BF theory].
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.
@ General: '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-in
[discussions with 't Hooft]; Kay & Larkin a0708.
@ General spacetimes: Bonelli PLB(99)ht/98;
Bousso JHEP(99)ht,
CQG(00)ht/99-in;
Tavakol & Ellis
PLB(99)ht.
@ Interpretations: Dance qp/04 [ito 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-in
[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 conj];
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
21 jun 2008