Kaluza-Klein Theories  

In General > s.a. higher-dimensional gravity.
* Idea: A (4+k)-dimensional general relativity (with matter in extended versions), and the usual Einstein-Hilbert action; The extra dimensions have to be all spacelike, otherwise one gets arbitrarily large causality violations and negative 4D energy density; The non-abelian theories often have torsion, if they include fermions.
* Dimensional reduction: An effective 4D theory can be obtained in a natural way if there are Killing vector fields along the extra dimensions; One gets gravity coupled to fields coming from the extra metric components (or, if there were already matter fields, they end up coupled to gauge fields); If there are no Killing vector fields, one does a harmonic mode expansion – this of course is coordinate-dependent; There are ambiguities in the choice of fields in 4D; Jordan proposed to solve them by experiment; usually it is done getting some desired form for the action; > s.a. spacetime models.
* Motivation: (1) One gets from a purely metric theory all the known interactions in 4D; The field strengths are components of the higher-dimensional Christoffel symbols; To get strong and electroweak interactions, one needs at least 11D; (2) Internal charges coupled to gauge fields are treated on the same footing as energy-momentum; (3) It arises naturally in supergravity theories; (4) Possible spacetime dependence of the gravitational and fine-structure constants (this really depends on the 4D interpretation adopted); (5) Lowering of GUT scale from 1016 to 103 GeV, if the internal dimension is large enough (> see branes).
* Problems: Chiral fermions (ok if there are matter fields); Renormalizability (as usual for gravity); Failure to reproduce quantum numbers of particles; Appearance of huge mass terms.

Early Work
* History: Kaluza suggested the use of an extra dimension; Klein that it be compactified.
@ "Constant internal radius": Nordström PZ(14)phy/07, OFVSF(14)phy/07, OFVSF(15)phy/07; Kaluza SPAW(21)-a1803; Einstein & Grommer SUBH(23); Klein ZP(26); Einstein SPAW(27), SPAW(27); Klein ZP(28); Einstein & Rosen PR(35); Einstein & Bergmann AM(38); Einstein, Bargmann & Bergmann in(41); Einstein & Pauli AM(43).
@ Variable radius: Jordan AN(48); Thiry CR(48), JMPA(51); in Lichnerowicz 55; Klein HPAS(56); Jordan ZP(59); in Wheeler 62; in DeWitt 65; Rayski APP(65); Kerner AIHP(68).
@ Non-Abelian: in DeWitt 65; Kerner AIHP(68); Trautman RPMP(70).
@ History: in Pais 82; Krym TMP(99)gq/98; O'Raifeartaigh & Straumann RMP(00)hp/98; Straumann gq/00-MG9 [Pauli and non-abelian Kaluza-Klein]; van Dongen SHPMP(02)gq/00 [Einstein 1938–1943]; Ravndal a1309 [Oskar Klein's contributions]; Peruzzi & Rocci a1811 [Einstein's 1927 papers]; > s.a. higher-dimensional gravity.

And Other Higher-Dimensional Theories > s.a. branes; higher-dimensional gravity; teleparallel theories.
@ Kaluza-Klein modes in brane world: Gu ap/03 [Kaluza-Klein bursts and cosmic rays].
@ With extra timelike dimensions: Yndurain PLB(91); Iglesias & Kakushadze PLB(01)ht/00; Ellis gq/01 [5D Kaluza-Weyl space].
@ With no extra dimensions: Pavšič PLB(05)ht/04, IJMPA(06)gq/05 [Clifford space].
@ Non-commutative: Madore in(89)-a1510 [supplementary factor in the algebra], PRD(90); Madore & Mourad ht/96; Besnard a1902; > s.a. non-commutative geometry.
@ Higher-order gravity theories: Maeda & Dadhich PRD(07)ht/06, Molina & Dadhich IJMPD(09)-a0804 [Einstein-Gauss-Bonnet gravity]; Dehghani & Assyyaee PLB(09)-a0811 [third-order Lovelock gravity, and dark energy]; Başkal & Kuyrukcu GRG(13)-a1004 [dimensional reduction].
@ Other variations: Cianfrani & Montani a0904-proc [based on an averaging procedure]; Kalinowski EPJC(14)-a1401, FdP(16)-a1410 [non-symmetric gravity]; Stoica IJMPD(16)-a1601 [degenerate metric, zero-length extra dimensions]; Collion & Vaugon a1709 [non-Ricci-flat geometries, including matter].

Special Aspects > see ADM formulation; black holes; CPT; energy positivity; models and phenomenology; spacetime topology and topology change.
@ Reduction: Grumiller & Jackiw IJMPD(06)mp [conformally flat spaces];
Lacquaniti & Montani MPLA(09)-a0906 [5D]; Gauntlett et al JHEP(09) [D = 11 supergravity]; Chopovsky et al AHEP(13)-a1311 [Ricci-flat internal spaces and absence of KK particles].

General References > s.a. particle physics; spacetime.
@ I: Kaku 94.
@ Textbooks and reviews: Hermann 78; Ferrara & Ellis 82; de Sabbata & Schmutzer 83; Chodos CNPP(84); Mecklenburg FdP(84); Lee 84; Freund PhyD(85); Piran & Weinberg ed-86; Appelquist et al ed-87; Bailin & Love RPP(87); Blau et al in(87); Coquereaux & Jadczyk 88; Duff ht/94; Overduin & Wesson PRP(97)gq/98; Wesson 99 [5D]; Cianfrani & Montani a0904-proc.
@ Mathematical aspects: Wesson MPLA(95) [Killing vector fields and covariance]; Betounes JGP(04) [Rab].
@ Related topics: Keyl CQG(97) [quantum field theory on Kaluza-Klein background]; Kane PT(98)may [fiction]; de Assis et al G&C(00) [loop variables]; Ponce de León G&C(02) [equation of motion]; Starks et al IJTP(06) [5D, geometric formulation]; Reifler & Morris a0707 [equivalence with Yang-Mills theory]; Lukman et al NJP(11)-a1001 [effective two-dimensionality].

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