Editing Supergravity (section)

==History==

===Gauge supersymmetry===
The first theory of local supersymmetry was proposed by [[Richard Arnowitt|Dick Arnowitt]] and [[Pran Nath (physicist)|Pran Nath]] in 1975<ref name="NathArnowitt">{{cite journal | last1 = Nath | first1 = P. | last2 = Arnowitt | first2 = R. | year = 1975 | title = Generalized Super-Gauge Symmetry as a New Framework for Unified Gauge Theories | journal = Physics Letters B | volume = 56 | issue = 2| page = 177 | doi=10.1016/0370-2693(75)90297-x| bibcode = 1975PhLB...56..177N }}</ref> and was called '''gauge supersymmetry'''.

===Supergravity===
The first model of 4-dimensional supergravity (without this denotation) was formulated by Dmitri Vasilievich Volkov and Vyacheslav A. Soroka in 1973,<ref name ="Volkov Soroka">{{cite journal | last1 = Volkov | first1 = D.V. | last2 = Soroka | first2 = V.A. | year = 1973 | title = Higgs effect for Goldstone particles with spin 1/2 | journal = JETP Letters | volume = 16 | issue = 11| pages = 438–440 | doi=10.1007/BFb0105271 | bibcode = 1973JETPL..18..312V }}</ref> emphasizing the importance of spontaneous supersymmetry breaking for the possibility of a realistic model. The [[Pure 4D N = 1 supergravity|minimal version of 4-dimensional supergravity]] (with unbroken local supersymmetry) was constructed in detail in 1976 by [[Daniel Z. Freedman|Dan Freedman]], [[Sergio Ferrara]] and [[Peter van Nieuwenhuizen]].<ref name="Summary">{{cite journal | last1 = Freedman | first1 = D.Z. | last2 = van Nieuwenhuizen | first2 = P. | last3 = Ferrara | first3 = S. | year = 1976 | title = Progress Toward A Theory Of Supergravity | journal =  Physical Review D| volume =  13| issue = 12| pages = 3214–3218 | doi=10.1103/physrevd.13.3214| bibcode = 1976PhRvD..13.3214F }}</ref>  In 2019 the three were awarded a special [[Breakthrough Prize in Fundamental Physics]] for the discovery.<ref>{{Cite news|url=https://www.cbc.ca/news/technology/supergravity-breakthrough-prize-1.5237900|title=Supergravity scientists share $3M US Breakthrough Prize|work=CBC News}}</ref> The key issue of whether or not the spin 3/2 field is consistently coupled was resolved in the nearly simultaneous paper, by [[Stanley Deser|Deser]] and [[Bruno Zumino|Zumino]],<ref name="DeserZumino">{{cite journal | last1 = Deser | first1 = S. | last2 = Zumino | first2 = B. | year = 1976 | title = Consistent Supergravity | url = https://cds.cern.ch/record/438874| journal =   Physics Letters B| volume =  62| issue = 3| pages = 335–337 | doi=10.1016/0370-2693(76)90089-7| bibcode =  1976PhLB...62..335D}}</ref> which independently proposed the minimal 4-dimensional model. It was quickly generalized to many different theories in various numbers of [[dimensions]] and involving additional (N) supersymmetries. Supergravity theories with N>1 are usually referred to as extended supergravity (SUEGRA). Some supergravity theories were shown to be related to certain [[higher-dimensional]] supergravity theories via [[compactification (physics)|dimensional reduction]] (e.g. N=1, 11-dimensional supergravity is dimensionally reduced on T<sup>7</sup> to 4-dimensional, ungauged, ''N'' = 8 supergravity). The resulting theories were sometimes referred to as [[Kaluza–Klein theory|Kaluza–Klein theories]] as Kaluza and Klein constructed in 1919 a 5-dimensional gravitational theory, that when dimensionally reduced on a circle, its 4-dimensional non-massive modes describe [[electromagnetism]] coupled to [[gravity]].

===mSUGRA===
mSUGRA means minimal SUper GRAvity. The construction of a realistic model of particle interactions within the ''N'' = 1 supergravity framework where supersymmetry (SUSY) breaks by a super [[Higgs mechanism]] carried out by [[Ali Chamseddine]], [[Richard Arnowitt]] and [[Pran Nath (physicist)|Pran Nath]] in 1982. Collectively now known as minimal supergravity Grand Unification Theories (mSUGRA GUT), gravity mediates the breaking of SUSY through the existence of a [[hidden sector]]. mSUGRA naturally generates the Soft SUSY breaking terms which are a consequence of the Super Higgs effect. Radiative breaking of electroweak symmetry through [[Renormalization]] Group Equations (RGEs) follows as an immediate consequence. 
Due to its predictive power, requiring only four input parameters and a sign to determine the low energy phenomenology from the scale of Grand Unification, it is widely investigated in [[particle physics]].
{{See also|Minimal_Supersymmetric_Standard_Model#Gravity-mediated_supersymmetry_breaking|label 1=Gravity-Mediated Supersymmetry Breaking in the MSSM}}

===11D: the maximal SUGRA===
{{Main|Eleven-dimensional supergravity}} 
One of these supergravities, the 11-dimensional theory, generated considerable excitement as the first potential candidate for the [[theory of everything]]. This excitement was built on four pillars, two of which have now been largely discredited:

* [[Werner Nahm]] showed<ref>{{cite journal | last1 = Nahm | first1 = Werner | year = 1978| title = Supersymmetries and their representations | url = https://cds.cern.ch/record/132743| journal = Nuclear Physics B | volume = 135 | issue = 1| pages = 149–166 | doi = 10.1016/0550-3213(78)90218-3 | bibcode = 1978NuPhB.135..149N}}</ref> 11 dimensions as the largest number of dimensions consistent with a single graviton, and more dimensions will show particles with spins greater than 2. However, if two of these dimensions are time-like, these problems are avoided in 12 dimensions. [[Itzhak Bars]]{{Citation needed|date=March 2007}} gives this emphasis.
* In 1981 [[Ed Witten]] showed<ref>{{cite journal | last1 = Witten | first1 = Ed | year = 1981| title = Search for a realistic Kaluza-Klein theory | journal = Nuclear Physics B | volume = 186 | issue = 3| pages = 412–428 | doi = 10.1016/0550-3213(81)90021-3 | bibcode = 1981NuPhB.186..412W}}</ref> 11 as the smallest number of dimensions big enough to contain the [[gauge group]]s of the [[Standard Model]], namely [[SU(3)]] for the [[strong interactions]] and [[SU(2)]] times [[U(1)]] for the [[electroweak]] interactions.{{citation needed|date=March 2013}} Many techniques exist to embed the standard model gauge group in supergravity in any number of dimensions like the obligatory gauge symmetry in [[type I string theory|type I]] and [[heterotic string theory|heterotic string theories]], and obtained in [[type II string theory]] by [[compactification (physics)|compactification]] on certain [[Calabi–Yau manifold]]s. The [[D-brane]]s engineer gauge symmetries too.
* In 1978 [[Eugène Cremmer]], [[Bernard Julia]] and [[Joël Scherk]] (CJS) found<ref>E. Cremmer, B. Julia and J. Scherk, "Supergravity theory in eleven dimensions", ''Physics Letters'' '''B76''' (1978)
pp 409-412,</ref> the classical action for an 11-dimensional supergravity theory. This remains today the only known classical 11-dimensional theory with local supersymmetry and no fields of spin higher than two.{{Citation needed|date=March 2007}} Other 11-dimensional theories known and quantum-mechanically inequivalent reduce to the CJS theory when one imposes the classical equations of motion. However, in the mid-1980s [[Bernard de Wit]] and [[Hermann Nicolai]] found an alternate theory in D=11 Supergravity with Local SU(8) Invariance. While not manifestly Lorentz-invariant, it is in many ways superior, because it dimensionally-reduces to the 4-dimensional theory without recourse to the classical equations of motion.

* In 1980 [[Peter Freund]] and [[M. A. Rubin]] showed that compactification from 11 dimensions preserving all the SUSY generators could occur in two ways, leaving only 4 or 7 macroscopic dimensions, the others compact.<ref>{{Cite journal
|author=Peter G.O. Freund
|author2=Mark A. Rubin
|date=1980
|title=Dynamics of dimensional reduction
|journal=Physics Letters B
|volume=97
|pages=233–235
|doi=10.1016/0370-2693(80)90590-0
|issue=2
|bibcode = 1980PhLB...97..233F }}</ref> The noncompact dimensions have to form an [[anti-de Sitter space]]. There are many possible compactifications, but the [[Freund-Rubin compactification]]'s invariance under all of the supersymmetry transformations preserves the action.

Finally, the first two results each appeared to establish 11 dimensions, the third result appeared to specify the theory, and the last result explained why the observed universe appears to be four-dimensional.

Many of the details of the theory were fleshed out by [[Peter van Nieuwenhuizen]], [[Sergio Ferrara]] and [[Daniel Z. Freedman]].

===The end of the SUGRA era===
The initial excitement over 11-dimensional supergravity soon waned, as various failings were discovered, and attempts to repair the model failed as well. Problems included:{{Citation needed|date=May 2016}}

* The compact manifolds which were known at the time and which contained the standard model were not compatible with supersymmetry, and could not hold [[quark]]s or [[lepton]]s. One suggestion was to replace the compact dimensions with the 7-sphere, with the symmetry group [[SO(8)]], or the squashed 7-sphere, with symmetry group [[SO(5)]] times [[SU(2)]].
* Until recently, the physical [[neutrino]]s seen in experiments were believed to be massless, and appeared to be left-handed, a phenomenon referred to as the [[Chirality (physics)|chirality]] of the Standard Model. It was very difficult to construct a chiral fermion from a compactification — the compactified manifold needed to have singularities, but physics near singularities did not begin to be understood until the advent of [[orbifold]] [[conformal field theory|conformal field theories]] in the late 1980s.
* Supergravity models generically result in an unrealistically large [[cosmological constant]] in four dimensions, and that constant is difficult to remove, and so require [[Fine-tuning (physics)|fine-tuning]]. This is still a problem today.
* Quantization of the theory led to quantum field theory [[gauge anomaly|gauge anomalies]] rendering the theory inconsistent. In the intervening years physicists have learned how to cancel these anomalies.

Some of these difficulties could be avoided by moving to a 10-dimensional theory involving [[superstring]]s. However, by moving to 10 dimensions one loses the sense of uniqueness of the 11-dimensional theory.<ref>{{cite arXiv |eprint=hep-th/9805177|last1=Duff|first1=M. J.|title=A Layman's Guide to M-theory|year=1998}}</ref>

The core breakthrough for the 10-dimensional theory, known as the [[first superstring revolution]], was a demonstration by [[Michael B. Green]], [[John H. Schwarz]] and [[David Gross]] that there are only three supergravity models in 10 dimensions which have gauge symmetries and in which all of the gauge and [[gravitational anomalies]] cancel. These were theories built on the groups [[SO(32)]] and <math>E_8 \times E_8</math>, the [[direct product of groups|direct product]] of two copies of [[E8 (mathematics)|E<sub>8</sub>]]. Today we know that, using [[D-branes]] for example, gauge symmetries can be introduced in other 10-dimensional theories as well.<ref name="Blumen">
{{cite journal
 |date=2005
 |title=Toward Realistic Intersecting D-Brane Models
 |arxiv=hep-th/0502005
 |last1=Blumenhagen| first1=R.
 |last2=Cvetic| first2=M.|author2-link= Mirjam Cvetič
 |last3=Langacker | first3=P.
 |last4=Shiu| first4=G. | doi=10.1146/annurev.nucl.55.090704.151541 | doi-access=free | volume=55 | issue=1 | journal=[[Annual Review of Nuclear and Particle Science]] | pages=71–139
|bibcode=2005ARNPS..55...71B|s2cid=15148429
 }}</ref>

===The second superstring revolution===
Initial excitement about the 10-dimensional theories, and the string theories that provide their quantum completion, died by the end of the 1980s. There were too many [[Calabi–Yau]]s to compactify on, many more than [[Shing-Tung Yau|Yau]] had estimated, as he admitted in December 2005 at the [[23rd International Solvay Conference in Physics]]. None quite gave the standard model, but it seemed as though one could get close with enough effort in many distinct ways. Plus no one understood the theory beyond the regime of applicability of string [[perturbation theory]].

There was a comparatively quiet period at the beginning of the 1990s; however, several important tools were developed. For example, it became apparent that the various superstring theories were related by "[[string dualities]]", some of which relate weak string-coupling - perturbative - physics in one model with strong string-coupling - non-perturbative - in another.

Then the [[second superstring revolution]] occurred. [[Joseph Polchinski]] realized that obscure string theory objects, called [[D-branes]], which he discovered six years earlier, equate to stringy versions of the [[p-branes]] known in supergravity theories. String theory perturbation didn't restrict these [[p-branes]]. Thanks to supersymmetry, p-branes in supergravity gained understanding well beyond the limits of string theory.

Armed with this new [[nonperturbative]] tool, [[Edward Witten]] and many others could show all of the perturbative string theories as descriptions of different states in a single theory that Witten named [[M-theory]]. Furthermore, he argued that M-theory's [[Long Wavelength Limit|long wavelength limit]], i.e. when the quantum wavelength associated to objects in the theory appear much larger than the size of the 11th dimension, needs 11-dimensional supergravity descriptors that fell out of favor with the [[first superstring revolution]] 10 years earlier, accompanied by the 2- and 5-branes.

Therefore, supergravity comes full circle and uses a common framework in understanding features of string theories, M-theory, and their compactifications to lower spacetime dimensions.