In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra a superalgebra, called the super-Poincaré algebra, gauging supersymmetry makes gravity arise in a natural way.
Like any field theory of gravity, a supergravity theory contains a spin-2 field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner. This field has spin 3/2 and its quantum is the gravitino. The number of gravitino fields is equal to the number of supersymmetries.
The minimal version of four-dimensional Supergravity was discovered in 1976 by Dan Freedman, Sergio Ferrara and Peter van Nieuwenhuizen, and 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 dimensional reduction (e.g. N=1, 11-dimensional supergravity is dimensionally reduced on T7 to four-dimensional, ungauged, N=8 Supergravity). The resulting theories were sometimes referred to as 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 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 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, its interest is a widely investigated model of particle physics
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:
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.
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:
Some of these difficulties could be avoided by moving to a 10-dimensional theory involving superstrings. However, by moving to 10 dimensions one loses the sense of uniqueness of the 11-dimensional theory.
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 , the direct product of two copies of E8. Today we know that, using D-branes for example, gauge symmetries can be introduced in other 10-dimensional theories as well.
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–Yaus to compactify on, many more than 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, i.e. when the quantum wavelength associated to objects in the theory appear much larger than the size of the 11th dimension, need 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.
The term "low energy limits" labels some 10-dimensional supergravity theories. These arise as the massless, tree-level approximation of string theories. True effective field theories of string theories, rather than truncations, are rarely available. Due to string dualities, the conjectured 11-dimensional M-theory is required to have 11-dimensional supergravity as a "low energy limit". However, this doesn't necessarily mean that string theory/M-theory is the only possible UV completion of supergravity; supergravity research is useful independent of those relations.
Before we move on to SUGRA proper, let's recapitulate some important details about general relativity. We have a 4D differentiable manifold M with a Spin(3,1) principal bundle over it. This principal bundle represents the local Lorentz symmetry. In addition, we have a vector bundle T over the manifold with the fiber having four real dimensions and transforming as a vector under Spin(3,1). We have an invertible linear map from the tangent bundle TM to T. This map is the vierbein. The local Lorentz symmetry has a gauge connection associated with it, the spin connection.
The following discussion will be in superspace notation, as opposed to the component notation, which isn't manifestly covariant under SUSY. There are actually many different versions of SUGRA out there which are inequivalent in the sense that their actions and constraints upon the torsion tensor are different, but ultimately equivalent in that we can always perform a field redefinition of the supervierbeins and spin connection to get from one version to another.
In 4D N=1 SUGRA, we have a 4|4 real differentiable supermanifold M, i.e. we have 4 real bosonic dimensions and 4 real fermionic dimensions. As in the nonsupersymmetric case, we have a Spin(3,1) principal bundle over M. We have an R4|4 vector bundle T over M. The fiber of T transforms under the local Lorentz group as follows; the four real bosonic dimensions transform as a vector and the four real fermionic dimensions transform as a Majorana spinor. This Majorana spinor can be reexpressed as a complex left-handed Weyl spinor and its complex conjugate right-handed Weyl spinor (they're not independent of each other). We also have a spin connection as before.
We will use the following conventions; the spatial (both bosonic and fermionic) indices will be indicated by M, N, ... . The bosonic spatial indices will be indicated by μ, ν, ..., the left-handed Weyl spatial indices by α, β,..., and the right-handed Weyl spatial indices by , , ... . The indices for the fiber of T will follow a similar notation, except that they will be hatted like this: . See van der Waerden notation for more details. . The supervierbein is denoted by , and the spin connection by . The inverse supervierbein is denoted by .
The supervierbein and spin connection are real in the sense that they satisfy the reality conditions
The covariant derivative is defined as
The covariant exterior derivative as defined over supermanifolds needs to be super graded. This means that every time we interchange two fermionic indices, we pick up a +1 sign factor, instead of -1.
The presence or absence of R symmetries is optional, but if R-symmetry exists, the integrand over the full superspace has to have an R-charge of 0 and the integrand over chiral superspace has to have an R-charge of 2.
A chiral superfield X is a superfield which satisfies . In order for this constraint to be consistent, we require the integrability conditions that for some coefficients c.
Unlike nonSUSY GR, the torsion has to be nonzero, at least with respect to the fermionic directions. Already, even in flat superspace, . In one version of SUGRA (but certainly not the only one), we have the following constraints upon the torsion tensor:
Here, is a shorthand notation to mean the index runs over either the left or right Weyl spinors.
The superdeterminant of the supervierbein, , gives us the volume factor for M. Equivalently, we have the volume 4|4-superform.
If we complexify the superdiffeomorphisms, there is a gauge where , and . The resulting chiral superspace has the coordinates x and Θ.
R is a scalar valued chiral superfield derivable from the supervielbeins and spin connection. If f is any superfield, is always a chiral superfield.
The action for a SUGRA theory with chiral superfields X, is given by
Unlike the case for flat superspace, adding a constant to either the Kähler or superpotential is now physical. A constant shift to the Kähler potential changes the effective Planck constant, while a constant shift to the superpotential changes the effective cosmological constant. As the effective Planck constant now depends upon the value of the chiral superfield X, we need to rescale the supervierbeins (a field redefinition) to get a constant Planck constant. This is called the Einstein frame.
N=8 Supergravity is the most symmetric quantum field theory which involves gravity and a finite number of fields. It can be found from a dimensional reduction of 11D supergravity by making the size of 7 of the dimensions go to zero. It has 8 supersymmetries which is the most any gravitational theory can have since there are 8 half-steps between spin 2 and spin -2. (A graviton has the highest spin in this theory which is a spin 2 particle). More supersymmetries would mean the particles would have superpartners with spins higher than 2. The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories). Stephen Hawking in his A Brief History of Time speculated that this theory could be the Theory of Everything. However, in later years this was abandoned in favour of String Theory. There has been renewed interest in the 21st century with the possibility that this theory may be finite.
Higher-dimensional SUGRA is the higher-dimensional, supersymmetric generalization of general relativity. Supergravity can be formulated in any number of dimensions up to eleven. Higher-dimensional SUGRA focuses upon supergravity in greater than four dimensions.
The number of supercharges in a spinor depends on the dimension and the signature of spacetime. The supercharges occur in spinors. Thus the limit on the number of supercharges cannot be satisfied in a spacetime of arbitrary dimension. Some theoretical examples in which this is satisfied are:
The supergravity theories that have attracted the most interest contain no spins higher than two. This means, in particular, that they do not contain any fields that transform as symmetric tensors of rank higher than two under Lorentz transformations. The consistency of interacting higher spin field theories is, however, presently a field of very active interest.
Bernard Julia (born 1952 in Paris) is a French theoretical physicist who has made contributions to the theory of supergravity. He graduated from Université Paris-Sud in 1978,
and is directeur de recherche with the CNRS working at the École Normale Supérieure. In 1978, together with Eugène Cremmer and Joël Scherk, he constructed 11-dimensional supergravity.
Shortly afterwards, Cremmer and Julia constructed the classical Lagrangian for four-dimensional N=8 supergravity by dimensional reduction from the 11-dimensional theory. Julia also studied spontaneous symmetry breaking and the Higgs mechanism in supergravityOther work includes a study, with A. Zee, of particles called dyons that carry both electric and magnetic charges
and many papers on string theory, M-theory, and dualities.
In 1986, Julia was awarded the Prix Paul Langevin of the Société Française de Physique.Dual graviton
In theoretical physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric-magnetic duality predicted by some formulations of supergravity in eleven dimensions.The dual graviton was first hypothesized in 1980. It was theoretically modeled in 2000s, which was then predicted in eleven-dimensional mathematics of SO(8) supergravity in the framework of electric-magnetic duality. It again emerged in the E11 generalized geometry in eleven dimensions, and the E7 generalized vielbeine-geometry in eleven dimensions. While there is no local coupling between graviton and dual graviton, the field introduced by dual graviton may be coupled to a BF model as non-local gravitational fields in extra dimensions.Gauged supergravity
Gauged supergravity is a supergravity theory in which some R-symmetry is gauged such that the gravitinos (superpartners of the graviton) are charged with respect to the gauge fields. Consistency of the supersymmetry transformation often requires
the presence of the potential for the scalar fields of the theory, or the cosmological constant if the theory
contains no scalar degree of freedom. The gauged supergravity often has the anti-de Sitter space as a supersymmetric vacuum.
Notable exception is a six-dimensional N=(1,0) gauged supergravity.
"Gauged supergravity" in this sense should be contrasted with Yang–Mills–Einstein supergravity in which some other would-be global symmetries of the theory are gauged and fields other than the gravitinos are charged with respect to the gauge fields.Glossary of string theory
This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.Gravitino
In supergravity theories combining general relativity and supersymmetry, the gravitino (G͂) is the gauge fermion supersymmetric partner of the hypothesized graviton. It has been suggested as a candidate for dark matter.
If it exists, it is a fermion of spin 3/2 and therefore obeys the Rarita-Schwinger equation. The gravitino field is conventionally written as ψμα with μ = 0, 1, 2, 3 a four-vector index and α = 1, 2 a spinor index.
For μ = 0 one would get negative norm modes, as with every massless particle of spin 1 or higher. These modes are unphysical, and for consistency there must be a gauge symmetry which cancels these modes: δψμα = ∂μεα, where εα(x) is a spinor function of spacetime. This gauge symmetry is a local supersymmetry transformation, and the resulting theory is supergravity.
Thus the gravitino is the fermion mediating supergravity interactions, just as the photon is mediating electromagnetism, and the graviton is presumably mediating gravitation. Whenever supersymmetry is broken in supergravity theories, it acquires a mass which is determined by the scale at which supersymmetry is broken. This varies greatly between different models of supersymmetry breaking, but if supersymmetry is to solve the hierarchy problem of the Standard Model, the gravitino cannot be more massive than about 1 TeV/c2.Higher-dimensional supergravity
Higher-dimensional supergravity is the supersymmetric generalization of general relativity in higher dimensions. Supergravity can be formulated in any number of dimensions up to eleven. This article focuses upon supergravity (SUGRA) in greater than four dimensions.Joël Scherk
Joël Scherk (French: [jɔɛl ʃɛʁk]; 1946 – 16 May 1980), often cited as Joel Scherk, was a French theoretical physicist who studied string theory and supergravity.M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at a string theory conference at the University of Southern California in the Spring of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution.
Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories appeared, at first, to be very different, work by several physicists showed that the theories were related in intricate and nontrivial ways. In particular, physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Witten's conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity.
Although a complete formulation of M-theory is not known, the theory should describe two- and five-dimensional objects called branes and should be approximated by eleven-dimensional supergravity at low energies. Modern attempts to formulate M-theory are typically based on matrix theory or the AdS/CFT correspondence.
According to Witten, M should stand for “magic”, “mystery”, or “membrane” according to taste, and the true meaning of the title should be decided when a more fundamental formulation of the theory is known.Investigations of the mathematical structure of M-theory have spawned important theoretical results in physics and mathematics. More speculatively, M-theory may provide a framework for developing a unified theory of all of the fundamental forces of nature. Attempts to connect M-theory to experiment typically focus on compactifying its extra dimensions to construct candidate models of our four-dimensional world, although so far none has been verified to give rise to physics as observed in high energy physics experiments.M2-brane
In theoretical physics, an M2-brane, is a spatially extended mathematical object (brane) that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular, it is a solution of eleven-dimensional supergravity which possesses a three-dimensional world volume.Michael Duff (physicist)
Michael James Duff FRS, FRSA is a British theoretical physicist and pioneering theorist of supergravity who is the Principal of the Faculty of Physical Sciences and Abdus Salam Chair of Theoretical Physics at Imperial College London.Ramond–Ramond field
In theoretical physics, Ramond–Ramond fields are differential form fields in the 10-dimensional spacetime of type II supergravity theories, which are the classical limits of type II string theory. The ranks of the fields depend on which type II theory is considered. As Joseph Polchinski argued in 1995, D-branes are the charged objects that act as sources for these fields, according to the rules of p-form electrodynamics. It has been conjectured that quantum RR fields are not differential forms, but instead are classified by twisted K-theory.
The adjective "Ramond–Ramond" reflects the fact that in the RNS formalism, these fields appear in the Ramond–Ramond sector in which all vector fermions are periodic. Both uses of the word "Ramond" refer to Pierre Ramond, who studied such boundary conditions (the so-called Ramond boundary conditions) and the fields that satisfy them in 1971.Ray William Johnson
Ray William Johnson (born August 14, 1981) is an American actor, comedian, film producer, film director, screenwriter, and rapper, who is known for his YouTube channel, Ray William Johnson, and his web series on that channel, Equals Three. As of March 2019, the channel had earned more than three billion views and 9.8 million subscribers, making it one of the most viewed channels on YouTube at the time. Johnson left the series in March 2014, but continued to produce it and other web series like Booze Lightyear, Comedians On, and Top 6, the first two of which were later cancelled.Toward the end of his tenure at Equals Three, Johnson began branching out into other mediums. His first scripted web series, Riley Rewind, premiered on Facebook in 2013. He created a television concept that was purchased by FX also in 2013. He made his live-action acting debut in the indie road film Who's Driving Doug alongside former Breaking Bad star RJ Mitte. Additionally, his production company, Mom & Pop Empires, is co-producing a documentary with Supergravity Pictures about monopolies in the cable television industry.Renata Kallosh
Renata Elizaveta Kallosh (Russian: Рената-Елизавета Эрнестовна Каллош), is a theoretical physicist. She is a Professor of Physics at Stanford University, working there on supergravity, string theory and inflationary cosmology.
She completed her Bachelor's from Moscow State University in 1966 and obtained her Ph.D. from Lebedev Physical Institute, Moscow in 1968. She was then a professor at the same institute, before moving to CERN for a year in 1989. Kallosh joined Stanford in 1990 and continues to work there. In 2009 she received the Lise Meitner Award of the Gothenburg University. In 2014 awarded Doctorate Honoris Causa of the University of Groningen. In 2017 she was awarded Lorentz Chair position at the University of Leiden, and became a member of the American Academy of Arts and Sciences.
Kallosh is best known for her contributions to the theory of supergravity---the supersymmetric generalization of Einstein's theory of gravity. She was the first to quantize supergravity, obtaining the full set of Feynman rules including a new, unexpected ghost particle (now called the Nielsen-Kallosh ghost). This paper also gave one of the first applications of BRST symmetry to express the gauge invariances of gravity, and, incidentally, introduced the name "BRST". She also was the first to understand the structure of divergences in quantum theories of supergravity, showing, among other results, that supergravity with N=8 supersymmetry is finite at least up to 8 loops. She is the author of many papers on black hole solutions in supergravity theories. A particularly influential work is the recognition, in collaboration with Sergio Ferrara, that black hole solutions with higher supersymmetry correspond to attractor solutions of analogue mechanical systems.Kallosh is also known for her contributions to string theory. In particular, she, along with Sandip Trivedi, Andrei Linde, and Shamit Kachru, found the mechanism to stabilize string theory vacua referred to as "KKLT" mechanism after the authors' last names. This mechanism provided a possible theoretical explanation of the anomalously small value of vacuum energy (cosmological constant), and a description of the present stage of the accelerated expansion of the universe in the context of the theory of inflationary multiverse and string theory landscape.After the discovery of the KKLT construction, her interests shifted towards investigation of cosmological implications of supergravity and string theory. In particular, Renata Kallosh and Andrei Linde, together with their collaborators, developed a theory of cosmological attractors. This is a broad class of versions of inflationary cosmology which provide one of the best fits to the latest observational data.Seifallah Randjbar-Daemi
Seifallah Randjbar-Daemi (Persian: سیف الله رنجبر دائمی, born 1950) is an Iranian theoretical physicist. He is Assistant Director and Head of High Energy, Cosmology and Astroparticle Physics Section at the International Centre for Theoretical Physics.
He received his PhD in 1980 from Imperial College London, University of London, UK. Seifallah Randjbar-Daemi's contributions are in the area of theoretical high energy physics, quantum field theory, superstring theory, supersymmetry and supergravity theories in all dimensions and cosmology.Sergio Ferrara
Sergio Ferrara (born May 2, 1945) is an Italian physicist working on theoretical physics of elementary particles and mathematical physics. He is renowned for the discovery of theories introducing supersymmetry as a symmetry of elementary particles (super-Yang–Mills theories, together with Bruno Zumino) and of supergravity, the first significant extension of Einstein's general relativity, based on the principle of "local supersymmetry" (together with Daniel Z. Freedman, and Peter van Nieuwenhuizen). He is an emeritus staff member at CERN and a professor at the University of California, Los Angeles.Supersymmetry breaking
In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking. In supergravity, this results in a slightly modified counterpart of the Higgs mechanism where the gravitinos become massive.
Supersymmetry breaking occurs at supersymmetry breaking scale. The superpartners, whose mass would otherwise be equal to the mass of the regular particles in the absence of the SUSY breaking, become much heavier.
In the domain of applicability of stochastic differential equations including, e.g, classical physics, spontaneous supersymmetry breaking encompasses such nonlinear dynamical phenomena as chaos, turbulence, pink noise, etc.Sylvester James Gates
Sylvester James Gates Jr. (born December 15, 1950), known as S. James Gates Jr. or Jim Gates, is an American theoretical physicist who works on supersymmetry, supergravity, and superstring theory. He retired from the physics department at the University of Maryland College of Computer, Mathematical, and Natural Sciences in 2017, and he is now the Ford Foundation Professor of Physics at Brown University. He was a University of Maryland Regents Professor and served on former President Barack Obama's Council of Advisors on Science and Technology.Type II string theory
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theories have the maximal amount of supersymmetry — namely 32 supercharges — in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet, they differ only in the choice of GSO projection.Type I string theory
In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and which contains not only closed strings, but also open strings.
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