Brane World: Spacetime as a Membrane in Higher Dimensions |

**In General**
> s.a. boundaries in field theory; cosmological constant;
modified general relativity [signature change]; membranes;
string theory.

* __Idea__: (4+*k*)-D models
of spacetime and matter, in which the extra dimensions are either compactified
but not small as in Kaluza-Klein models, with size \(R \gg l_{\rm P}\), or
non-compact; The usual spacetime is a 4D brane, or a set of closely stacked
parallel ones, and the bulk is usually assumed to be flat or have constant
curvature; Ordinary matter corresponds to open strings, trapped on the brane
because they must have endpoints there; Only gravitons, which correspond to
closed strings, propagate off the brane (and get a mass in 4D) – might
explain why gravity is so weak at large scales.

* __Motivation__: The 4D Planck
mass could be much smaller than the 4 + *n* one,
*m*_{(4)}^{2}
= *R*^{n}
*m*_{(4+n)}^{2+n},
and unification could occur at small energies, ~ 10 TeV (2000, experiments
already put a lower bound at 1300 GeV); Could solve the hierarchy problem
without supersymmetry [this hope does not seem to be realized], and the
standard cosmological model problems without inflation.

* __History__: 1990, Joseph Polchinski
and others developed the theory of branes and showed that they are essential
to string theory.

* __Types of models__: Flat or warped;
Compact or non-compact extra dimensions; Untwisted or twisted (e.g., Randall-Sundrum).

* __Bounds on extra dimensions__: 2002, the
strongest bounds come from astrophysics and cosmology, rather than collider experiments;
The hierarchy problem could be solved only if there are at least 4 extra dimensions.

> __Online resources__:
see Wikipedia page.

**Matter Phenomenology** > s.a. brane cosmology
and gravity; higher-dimensional
theories; matter in quantum gravity;
string phenomenology.

* __Idea__: The constants
of nature we see are just shadows of the higher-dimensional ones, and can vary
in time and space, if the size of the extra dimensions varies; Constraints
on deviations from Newtonian gravity put upper bounds on the extra scales;
Constraints on Casimir effect contributions to the cosmological constant put
lower bounds on them.

* __High-energy phenomenology__:
2000, The idea does not contradict observations if the size of the extra dimensions
is up to about 0.1 mm; Better measurements of gravity at smaller scales may put
tighter bounds; Predicts non-trivial spacetime foamy refractive index for photons
and other massless probes; 2001, Possible formation of black holes in the TeV
realm of the LHC or high energy cosmic ray interactions.

@ __High-energy physics__:
Dvali et al MPLA(00),
Youm PRD(00)ht [4D forces];
Abbott et al (D0) PRL(01) [*p*-bar
*p* → *e*^{+}*e*^{−}
or *γγ*];
Shaposhnikov & Tinyakov PLB(01)ht,
Dvali et al PRD(02)ht/01 [Higgs alternative];
Kazanas & Nicolaidis GRG(03)hp/01 [cosmic ray spectrum];
Cheung ht/03-conf;
Nicolaidis & Sánchez MPLA(05)hp/03;
Cembranos et al IJMPD(04)hp-GRF [dark matter];
Choudhury et al JHEP(04) [Higgs production];
Aquino et al PRL(07) [at LHC];
Jalalzadeh et al PS(07) [4D forces].

@ __Neutrino oscillations__:
Dvali & Smirnov NPB(99);
Davoudiasl et al PRD(02)hp [bounds].

@ __Supersymmetry breaking__:
de Boer et al NPB(98) [dynamical];
Bagger et al JHEP(02)ht/01;
Anisimov et al PRD(02).

@ __Bounds from astrophysics__: Hannestad & Raffelt PRL(01)hp [gamma rays from supernovas],
PRL(02)hp/01 [neutron stars];
González et al a1601 [compact stars].

@ __Other astrophysics__:
Barger et al PLB(99) [supernovas];
Sigurdsson IJMPD(01)ap [*R* ≈ 80 micron from dust aggregation];
Gnedin ap/01 [photon propagation and TeV physics];
Burgess et al JHEP(02)hp [graviton dispersion];
> s.a. black-hole phenomenology.

@ __Other phenomenology__: Cardoso et al PRD(06)ht [diffraction radiation];
Berenji et Fermi-LAT JCAP(12)-a1201 [neutron stars];
Berezhiani & Nesti EPJC(12),
Sarrazin et al PLB(12)-a1201
+ news popsci(12)jan,
io9(12)jun ["neutron loss" or disappearance].

> __Related topics__: see
black-hole radiation; cosmic strings;
dark matter; kaluza-klein theory;
lensing; particles;
quantum particles; solitons.

**Randall-Sundrum Models** > s.a. black-hole formation;
brane cosmology; higgs mechanism;
torsion.

* __Idea__: The extra dimensions
are compactified, the usual spacetime is a 4D hypersurface or brane, and the bulk
spacetime is AdS; Need a large Λ < 0; Motivated by claims that it solves
the hierarchy problem.

@ __And matter__: Mavromatos & Rizos PRD(00)ht [strings];
Huber & Shafi PLB(01) [masses, couplings];
Ichinose PRD(02)ht [fermions];
Abazov et D0 PRL(05) [experimental search for gravitons].

@ __And supersymmetry__: Duff et al JMP(01)ht/00,
NPB(01)ht/00.

**References** > s.a. cosmological
perturbations; quantum field theory in curved backgrounds;
supersymmetry in field theory.

@ __I__:
Abel & March-Russell pw(00)nov;
Kaku 04;
Webb 04;
Burgess & Quevedo SA(07)nov [as interacting multiverse];
Kakushadze a1410.

@ __Intros, reviews__: Rubakov PU(01);
Maartens in(01)gq;
Dick CQG(01)ht;
Arkani-Hamed et al PT(02)feb;
Förste FdP(02)ht/01 [and strings];
Maartens LRR(04);
Durrer AIP(05)ht;
Johnson 06;
West 12;
Raychaudhuri & Sridhar 16 [particle physics].

@ __Precursors__: Pavšič PLA(86)gq/01;
Gibbons & Wiltshire NPB(87)ht/01;
Duff ht/04-in,
a1812-ln,
a1906-ln [historical].

@ __Theory__: Polchinski PRL(95)ht [D-branes];
Wesson et al IJMPA(96) [5D];
Dienes et al PLB(98)hp [unification scales];
Ponce de León MPLA(01)gq [vs spacetime-matter];
Rador EPJC(07)ht/05 [stabilization of extra dimensions];
Bergman & Lifschytz PLB(06)ht;
Berman PRP(08) [interactions, in M-theory].

@ __Non-compact extra dimensions__:
Arkani-Hamed et al PRL(00).

@ __In supergravity__: Stelle ht/97-ln;
Marolf RMF(03)gq/01-ln [11D supergravity].

@ __Bounds on extra dimensions__: Milton G&C(02)ht/01-in,
et al MPLA(01);
Uehara MPLA(02) [rev].

@ __Spacetime structure__: Mavromatos gq/00-conf [foam/optical properties];
Giddings PRD(03)ht [instability of 4D];
Greene et al PRD(13)-a1212 [3 as the
maximum number of spatial dimensions that can grow large cosmologically from an initial thermal fluctuation].

@ __Dynamics__: Diemand et al ht/01,
Carroll et al PRD(02)ht/01 [(in)stability];
Coley PRD(02)ht/01 [initial singularity].

@ __Thermodynamics__: Townsend & Zamaklar CQG(01)ht [first law].

@ __Variations__: Berezhiani et al PLB(01)ht [extra timelike directions];
Grady TQGR-ht/01 [3D phase boundary in 4D];
Henty ht/01 [5D bulk BF];
Kar gq/02 [asymmetrically warped 5D];
Durrer et al PLB(05)ht [D3 branes in 9+1 bulk];
Hinterbichler et al PLB(12)-a1101 [braneless scenario].

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send feedback and suggestions to bombelli at olemiss.edu – modified 20 jun 2019