Supergravity| Supergravity |
In General > s.a. Hypergravity; supersymmetry
phenomenology.
* History: 1976, Proposed
by Ferrara, Van Nieuwenhuizen & Freedman,
and independently by Deser & Zumino; 2007, Indications that N = 8 supergravity
may be perturbatively finite.
* Idea: A supergravity
theory is a supersymmetric field theory in which supersymmetry is made into
a local symmetry; It can be considered as another quantum field theory with
special fields, or as a theory in superspace, with bosonic and fermionic
(Grassmannian) coordinates, respectively (x, y, z, t)
and 
^{
i}, =
1... 4, i =
1 ... N.)
* Particle content and sectors:
It involves fields of spin 0, 1/2, 1, 3/2 (gravitino; these are consistent
only in sugra) and 2, and can
only be implemented when gravity (curvature) is present; It has
an observable sector with the standard model particles and their supersymmetric
partners,
and a hidden sector, coupled only gravitationallly to the observable
one.
* Motivation: It was
hoped that it would be a finite theory, because of cancellations, similarly
to what happened for some supersymmetric gauge theories,
but
this hope has not materialized – it is non-renormalizable at three-loop
level (does extended – N > 1 – supergravity offer hope?);
It is a framework for the unification of all interactions.
* Features: It incorporates torsion, related to intrinsic angular
momentum.
* Solutions: Any solution
of a supergravity model contains an exact solution of the regular Einstein
equation (with
a peculiar coupling).
Versions > s.a. 2D
gravity and 2D quantum gravity; Gauge
Gravity; gödel
spacetime;
higher-order; topological; unimodular
gravity.
* Most promising: N =
1 in 10D, with super-Yang-Mills fields.
* N = 1:
Fermions and bosons come in pairs; The irreps of the supersymmetry algebra
are doublets of spin 0-(1/2), (1/2)-1, (3/2)-2 (Majorana
gravitino-graviton);
There can be any number of these, but 1-(3/2) doublets
give extended
supergravity.
* N = 2:
Unifies electromagnetism and gravity by adding a complex (Dirac) gravitino
to the graviton, into one superparticle.
* N < 8:
Generalized general relativity with 1 graviton and N gravitinos,
rotating into each other under susy or global U(N).
* N > 8:
Phenomenology no good; Higher spins (> 2) and more
than 1 graviton.
@ N = 1: Chee GRG(98),
Fülöp CQG(94)gq/93 [self-dual
and anti-self-dual]; Page ht/93 [inconsistency];
Bagger et al NPB(01)ht/00 [4D,
Einstein-frame quantum inconsistency]; Ling & Smolin
PRD(01)ht/00 [holographic].
@ N = 2: Ferrara & van Nieuwenhuizen PRL(76).
@ N = 8: Bern et al PLB(07)
[uv finiteness], PRL(07) [perturbative finiteness].
@ N > 8: Nicolai & Samtleben NPB(98)ht [2D, N =
16]; Nishino & Gates CQG(00)ht/99 [type IIA*].
@ Broken sugra and super-Higgs: Deser & Zumino PRL(77);
Cremmer et al PLB(79).
@ Conformal sugra: Lindström & Rocek PRL(89);
Chee & Jia
GRG(01)gq/00 [Ashtekar
variables].
@ Self-dual sugra: Devchand & Ogievetsky NPB(95).
@ 11-dimensional: Deser ht/98-in;
Ling & Smolin NPB(01)ht/00 [as
constrained topological field theory]; Miemiec & Schnakenburg FdP(06)ht/05 [rev].
@ Other versions: Deser & Kay PLB(83)
[topologically massive]; Duff et al PRP(86)
[Kaluza-Klein version];
García-Compeán et al PRD(99)ht/98,
[MacDowell-Mansouri theory, dual]; Chandia et al ht/99-in
[Chern-Simons version]; Julia & Silva JHEP(00)ht/99 [first-order];
Binétruy et al PRP(01)
[couplings]; Salgado et al
PRD(02)gq/01 [Poincaré invariant
4D]; Djeghloul & Tahiri MPLA(00)ht/02 [quantum
action]; Allen ht/03-in
[Lorentz-violating]; van Nieuwenhuizen ht/04-in
[simple model]; Celi et al PRD(05)ht/04 [fake
sugra]; Giacomini et al CQG(07)ht/06
[3D].
References > s.a. branes; particle
types [gravitino]; string
phenomenology;
susy phenomenology.
@ Precursor: Rarita & Schwinger PR(41); & Volkov & Soroka
[Soroka ht/01-in].
@ General: Freedman et al PRD(76);
Deser & Zumino PLB(76);
Grisaru PLB(77);
Deser et al PRL(77), PRD(77);
Tabensky & Teitelboim PLB(77)
[from sqrt of general relativity]; Ferrara & van
Nieuwenhuizen PLB(78),
PLB(78),
PLB(78);
Baranov et al TMP(85);
Brandt FdP(02)ht-ln;
de Wit ht/02-ln;
van Nieuwenhuizen ht/04-in
[intro]; Gauntlett ht/05-in
[classifying solutions].
@ Textbooks and reviews: van Nieuwenhuizen in(77); Freedman & van
Nieuwenhuizen SA(79)feb; van Nieuwenhuizen & Freedman ed-79; Ferrara pr(80);
Hawking & Rocek
81; Cremmer in(81); van Nieuwenhuizen PRP(81); Julia 85; Castellani et al 86;
Jacob ed-86; Srivastava 86; Gibbons pr; Casati et al 91; Buchbinder & Kuzenko
95 [IIIb]; Tanii ht/98 [various
dimensions]; Van Proeyen ht/03-in.
@ Dimensional reduction: Lavrinenko et al CQG(98).
@ Solutions:
Gauntlett et al CQG(03)
[5D]; Gutowski et al CQG(03)
[6D]; > s.a. black holes; general
relativity solutions, instantons,
monopoles, solitons;
topological defects.
@ Boundary conditions:
Hawking PLB(83);
Esposito PLB(96);
Belyaev JHEP(06)
[with boundary]; van Nieuwenhuizen & Vassilevich CQG(05)ht; Van
Nieuwenhuizen
et
al IJMPD(06).
@ And spacetime symmetries: Vandyck GRG(88),
GRG(88), GRG(89), GRG(90), GRG(93); > s.a. symmetry.
@ FRW cosmology: Bertolami & Schiappa CQG(99)gq/98 [N =
1]; Tkach et al CQG(99)
[with complex scalar].
@ Other cosmology: Kallosh ht/02-in
[rev]; > s.a. AdS;
bianchi I and bianchi
IX; cosmology [future]; quintessence.
@ Quantization, perturbative: Bern et al PRD(08) [possible uv finiteness].
@ Related topics: Ferrara et al NPB(76)
[matter couplings].
Canonical Form and Quantization > s.a. [approaches
to quantum gravity]; renormalization; time
in quantum gravity.
@ Classical: Pilati NPB(78).
@ Euclidean: Vancea PRL(97),
Ciuhu & Vancea IJMPA(00)gq/98 [observables,
ito Dirac eigenvalues].
@ Constraints: Teitelboim PRL(77);
Gorobey & Lukyanenko CQG(89) [complex self-dual, closure of constraints]; Wulf IJMPD(97)gq/96 [N =
1, non-closure]; Pauna & Vancea
MPLA(98)
[ito Dirac eigenvalues].
@ Canonical quantization: Fradkin & Vasiliev
PLB(77);
D'Eath PRD(84);
Carroll et al NPB(94)ht [physical
states]; D'Eath IJMPD(96).
@ Connection / loop variables: Jacobson CQG(88);
Gorobey & Lukyanenko
CQG(90);
Matschull CQG(94);
Ezawa PTP(96)ht/95 [as
BF theory]; Armand-Ugón
et al NPB(96)ht/95 [loop
variables]; Nieto et al PRL(96)
[self-dual spin connection]; Urrutia ht/96-in;
Melosch & Nicolai
PLB(98)ht/97;
Ootsuka et al CQG(99)gq/98 [N =
2]; Tsuda & Shirafuji
CQG(99)gq/98,
PRD(00)gq [N =
2]; Ling & Smolin PRD(00)ht/99,
Ling JMP(02)ht/00-MG9
[spin networks]; Tsuda PRD(00)gq/99 [N =
1]; Tsuda
gq/04 [N =
3 chiral]; Kaul PRD(08)-a0711 [Holst
action with Immirzi parameter, no change in equations of motion].
> Spacific models: see gowdy
spacetime; graviton; minisuperspace.
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
11 jul 2008