In General > s.a. approaches to quantum gravity / Hypergravity; supersymmetry phenomenology; versions of supergravity and phenomenology.
* History: 1976, Proposed by Ferrara, Van Nieuwenhuizen & Freedman, and independently by Deser & Zumino; 2007 and 2009, Indications that N = 8 supergravity may be perturbatively finite.
* Idea: A supergravity theory is a supersymmetric field theory in which supersymmetry is made local; It can be considered as a quantum field theory with special fields, or as a theory in superspace with bosonic and fermionic (Grassmannian) coordinates, respectively (x, y, z, t) and θα i, α = 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 supergravity) 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).

References > s.a. grand unified theories; particle types [gravitino]; string phenomenology; topology in physics.
@ Precursor: Rarita & Schwinger PR(41); & Volkov & Soroka [Soroka ht/01-proc].
@ 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 FdP(05)ht-in [classifying solutions]; Coimbra et al a1107 [as generalised geometry]; Nastase a1112-ln [intro]; Ferrara & Marrani a1201-proc; Castellani et al a1607 [action as an integral on a supermanifold].
@ History: Ferrara a1701-proc; Ferrara & Sagnotti a1702-talk; Deser a1704.
@ Textbooks and reviews: van Nieuwenhuizen in(77); Freedman & van Nieuwenhuizen SA(78)feb; van Nieuwenhuizen & Freedman ed-79; Ferrara pr(80); Hawking & Roček ed-81; Cremmer in(81); van Nieuwenhuizen PRP(81); Julia in(85); Castellani et al 86; Jacob ed-86; Srivastava 86; Gibbons in(85); West 90; Casati et al 91; Wess & Bagger 92; Buchbinder & Kuzenko 95 [IIIb]; Tanii ht/98 [various dimensions]; Van Proeyen ht/03-proc; Freedman & Van Proeyen FdP(11)-a1106-ln, 12; Derendinger JPCS(15)-a1509; Nath 16.
@ Dimensional reduction: Lavrinenko et al CQG(98).
@ 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).
@ Related topics: Ferrara et al NPB(76) [matter couplings]; de Wit & van Zalk GRG(09) [and M-theory]; > s.a. positive-energy theorems.
> Online references: see Wikipedia page.

Canonical Form and Quantization > s.a. time in quantum gravity; types of quantum field theories [spin-3/2].
@ Classical: Pilati NPB(78).
@ Euclidean: Vancea PRL(97), Ciuhu & Vancea IJMPA(00)gq/98 [observables, in terms of 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) [in terms of Dirac eigenvalues]; McKeon a1203 [N = 1 supergravity in 2 + 1 dimensions, quantization]; Cvetič et al JHEP(15)-a1411 [explicit solutions of the (time-symmetric) initial-value constraints].
@ 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 AIP(96)ht; 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, Szczachor a1202-conf [Holst action with Immirzi parameter, no change in equations of motion]; Sengupta & Kaul PRD(10)-a0909; Bodendorfer et al CQG(13)-a1105, CQG(13)-a1105, PLB(12)-a1106; Bodendorfer a1509 [and the AdS/cft correspondence]; > s.a. models in canonical gravity.
@ Quantization, perturbative: Bern et al PRD(08) [possible UV finiteness]; Modesto a1206 [non-local, power-counting super-renormalizable and tree-level unitary theory]; Garousi PRD(13)-a1303 [Riemann curvature corrections].
@ Related topics: Deser et al PRL(77)-a1506 [renormalizability]; Bhattacharyya et al CQG(14) [one-loop test].
> Specific models: see gowdy spacetime; graviton; minisuperspace.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 20 apr 2017