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 = Rn 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 pe+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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