In supergravity theories combining general relativity and supersymmetry, the gravitino (

) 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.

CompositionElementary particle

Electric chargee

Gravitino cosmological problem

If the gravitino indeed has a mass of the order of TeV, then it creates a problem in the standard model of cosmology, at least naïvely.[1][2][3][4]

One option is that the gravitino is stable. This would be the case if the gravitino is the lightest supersymmetric particle and R-parity is conserved (or nearly so). In this case the gravitino is a candidate for dark matter; as such gravitinos will have been created in the very early universe. However, one may calculate the density of gravitinos and it turns out to be much higher than the observed dark matter density.

The other option is that the gravitino is unstable. Thus the gravitinos mentioned above would decay and will not contribute to the observed dark matter density. However, since they decay only through gravitational interactions, their lifetime would be very long, of the order of Mpl2m3 in natural units, where Mpl is the Planck mass and m is the mass of a gravitino. For a gravitino mass of the order of TeV this would be 105 s, much later than the era of nucleosynthesis. At least one possible channel of decay must include either a photon, a charged lepton or a meson, each of which would be energetic enough to destroy a nucleus if it strikes one. One can show that enough such energetic particles will be created in the decay as to destroy almost all the nuclei created in the era of nucleosynthesis, in contrast with observations. In fact, in such a case the universe would have been made of hydrogen alone, and star formation would probably be impossible.

One possible solution to the cosmological gravitino problem is the split supersymmetry model, where the gravitino mass is much higher than the TeV scale, but other fermionic supersymmetric partners of standard model particles already appear at this scale.

Another solution is that R-parity is slightly violated and the gravitino is the lightest supersymmetric particle. This causes almost all supersymmetric particles in the early Universe to decay into Standard Model particles via R-parity violating interactions well before the synthesis of primordial nuclei; a small fraction however decay into gravitinos, whose half-life is orders of magnitude greater than the age of the Universe due to the suppression of the decay rate by the Planck scale and the small R-parity violating couplings.[5]

See also


  1. ^ T. Moroi, H. Murayama Cosmological constraints on the light stable gravitino Phys.Lett.B303:289–294,1993
  2. ^ N. Okada, O. Seto A brane world cosmological solution to the gravitino problem Phys. Rev. D 71:023517,2005
  3. ^ A. de Gouvea, T. Moroi, H. Murayama Cosmology of Supersymmetric Models with Low-energy Gauge Mediation Phys. Rev. D 56:1281–1299,1997
  4. ^ M. Endo Moduli Stabilization and Moduli-Induced Gravitino Problem talk given at SUSY’06, 12 June 2006
  5. ^ F. Takayama and M. Yamaguchi, Phys. Lett. B 485 (2000)
Cold dark matter

In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. Observations indicate that approximately 85% of the matter in the universe is dark matter, with only a small fraction being the ordinary baryonic matter that composes stars, planets, and living organisms. Cold refers to the fact that the dark matter moves slowly compared to the speed of light, while dark indicates that it interacts very weakly with ordinary matter and electromagnetic radiation.

The physical nature of CDM is currently unknown, and there are a wide variety of possibilities. Among them are a new type of weakly interacting massive particle, primordial black holes, and axions.

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.

Gauge boson

In particle physics, a gauge boson is a force carrier, a bosonic particle that carries any of the fundamental interactions of nature, commonly called forces. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles.

All known gauge bosons have a spin of 1. Therefore, all known gauge bosons are vector bosons.

Gauge bosons are different from the other kinds of bosons: first, fundamental scalar bosons (the Higgs boson); second, mesons, which are composite bosons, made of quarks; third, larger composite, non-force-carrying bosons, such as certain atoms.


In supersymmetry theories of particle physics, a gaugino is the hypothetical fermionic supersymmetric field quantum (superpartner) of a gauge field, as predicted by gauge theory combined with supersymmetry. All gauginos have spin 1/2, except for gravitino (spin 3/2).

In the minimal supersymmetric extension of the standard model the following gauginos exist:

The gluino (symbol g͂) is the superpartner of the gluon, and hence carries color charge.

The gravitino (symbol G͂) is the supersymmetric partner of the graviton.

Three winos (symbol W͂± and W͂3) are the superpartners of the W bosons of the SU(2)L gauge fields.

The bino is the superpartner of the U(1) gauge field corresponding to weak hypercharge.Sometimes the term "electroweakinos" is used to refer to winos and binos and on occasion also higgsinos.


The goldstino is the Nambu−Goldstone fermion emerging in the spontaneous breaking of supersymmetry. It is the close fermionic analog of the Nambu−Goldstone bosons controlling the spontaneous breakdown of ordinary bosonic symmetries.

As in the case of Goldstone bosons, it is massless, unless there is, in addition, a small explicit supersymmetry breakdown involved, on top of the basic spontaneous breakdown; in this case it develops a small mass, analogous to that of Pseudo-Goldstone bosons of chiral symmetry breaking.

In theories where supersymmetry is a global symmetry, the goldstino is an ordinary particle (possibly the lightest supersymmetric particle, responsible for dark matter).

In theories where supersymmetry is a local symmetry, the goldstino is absorbed by the gravitino, the gauge field it couples to, becoming its longitudinal component, and giving it nonvanishing mass. This mechanism

is a close analog of the way the Higgs field gives nonzero mass to the W and Z bosons.

Vestigial bosonic superpartners of the goldstinos, called sgoldstinos, might also appear, but need not, as supermultiplets have been reduced to arrays. In effect, SSB of supersymmetry, by definition, implies a nonlinear realization of the supersymmetry in the Nambu−Goldstone mode, in which the goldstino couples identically to all particles in these arrays, and is thus the superpartner of all of them, equally.


In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravity. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity. In string theory, believed to be a consistent theory of quantum gravity, the graviton is a massless state of a fundamental string.

If it exists, the graviton is expected to be massless because the gravitational force is very long range and appears to propagate at the speed of light. The graviton must be a spin-2 boson because the source of gravitation is the stress–energy tensor, a second-order tensor (compared with electromagnetism's spin-1 photon, the source of which is the four-current, a first-order tensor). Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way that gravitational interactions do. This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton.

G̃ (disambiguation)

G̃ or g̃ is the letter G with a tilde.

G̃ or g̃ may also mean:

g̃, a gluino

G̃, a gravitino

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.

Kim Jihn-eui

Kim Jihn-eui (born July 30, 1946) is a South Korean theoretical physicist. His research interests concentrate on particle physics and cosmology and has many contributions to the field, most notably the suggestion of the invisible axion.

Lightest Supersymmetric Particle

In particle physics, the lightest supersymmetric particle (LSP) is the generic name given to the lightest of the additional hypothetical particles found in supersymmetric models. In models with R-parity conservation, the LSP is stable; in other words, the LSP cannot decay into any Standard Model particle, since all SM particles have the opposite R-parity. There is extensive observational evidence for an additional component of the matter density in the Universe that goes under the name dark matter. The LSP of supersymmetric models is a dark matter candidate and is a weakly interacting massive particle (WIMP).

List of particles

This article includes a list of the different types of atomic and sub-atomic particles found or hypothesized to exist in the whole of the universe, categorized by type. Properties of the various particles listed are also given, as well as the laws that the particles follow. For individual lists of the different particles, see the list below.

Minimal Supersymmetric Standard Model

The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the [minimum] number of new particle states and new interactions consistent with phenomenology". Supersymmetry pairs bosons with fermions, so every Standard Model particle has a superpartner yet undiscovered. If we find these superparticles, it equates to discovering such particles as dark matter, could provide evidence for grand unification, and provide hints as to whether string theory describes nature. The failure to find evidence for supersymmetry using the Large Hadron Collider suggests a leaning to abandon it.

Proton decay

In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.According to the Standard Model, protons, a type of baryon, are stable because baryon number (quark number) is conserved (under normal circumstances; see chiral anomaly for exception). Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon. Positron emission – a form of radioactive decay which sees a proton become a neutron – is not proton decay, since the proton interacts with other particles within the atom.

Some beyond-the-Standard Model grand unified theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles, or new X bosons with a half-life of 1031 to 1036 years. To date, all attempts to observe new phenomena predicted by GUTs (like proton decay or the existence of magnetic monopoles) have failed.

Quantum gravity (via virtual black holes and Hawking radiation) may also provide a venue of proton decay at magnitudes or lifetimes well beyond the GUT scale decay range above, as well as extra dimensions in supersymmetry.

There are theoretical methods of baryon violation other than proton decay including interactions with changes of baryon and/or lepton number other than 1 (as required in proton decay). These included B and/or L violations of 2, 3, or other numbers, or B − L violation. Such examples include neutron oscillations and the electroweak sphaleron anomaly at high energies and temperatures that can result between the collision of protons into antileptons or vice versa (a key factor in leptogenesis and non-GUT baryogenesis).


R-parity is a concept in particle physics. In the Minimal Supersymmetric Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings in the theory. Since baryon number and lepton number conservation have been tested very precisely, these couplings need to be very small in order not to be in conflict with experimental data. R-parity is a symmetry acting on the Minimal Supersymmetric Standard Model (MSSM) fields that forbids these couplings and can be defined as

or, equivalently, as

where s is spin, B is baryon number, and L is lepton number. All Standard Model particles have R-parity of +1 while supersymmetric particles have R-parity of −1.

Rarita–Schwinger equation

In theoretical physics, the Rarita–Schwinger equation is the relativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introduced by William Rarita and Julian Schwinger in 1941.

In modern notation it can be written as:

where is the Levi-Civita symbol, and are Dirac matrices, is the mass, , and is a vector-valued spinor with additional components compared to the four component spinor in the Dirac equation. It corresponds to the (1/2, 1/2) ⊗ ((1/2, 0) ⊕ (0, 1/2)) representation of the Lorentz group, or rather, its (1, 1/2) ⊕ (1/2, 1) part.

This field equation can be derived as the Euler–Lagrange equation corresponding to the Rarita–Schwinger Lagrangian:

where the bar above denotes the Dirac adjoint.

This equation controls the propagation of the wave function of composite objects such as the delta baryons (
) or for the conjectural gravitino. So far, no elementary particle with spin 3/2 has been found experimentally.

The massless Rarita–Schwinger equation has a fermionic gauge symmetry: is invariant under the gauge transformation , where is an arbitrary spinor field. This is simply the local supersymmetry of supergravity, and the field must be a gravitino.

"Weyl" and "Majorana" versions of the Rarita–Schwinger equation also exist.


A sgoldstino is any of the spin-0 superpartners of the goldstino in relativistic quantum field theories with spontaneously broken supersymmetry. The term sgoldstino was first used in 1998.In 2016, Petersson and Torre hypothesized that a sgoldstino particle might be responsible for the observed 750 GeV diphoton excess observed by Large Hadron Collider experiments.

Split supersymmetry

In particle physics, split supersymmetry is a proposal for physics beyond the Standard Model. It was proposed separately in three papers. The first by James Wells in June 2003 in a more modest form that mildly relaxed the assumption about naturalness in the Higgs potential. In May 2004 Nima Arkani-Hamed and Savas Dimopoulos argued that naturalness in the Higgs sector may not be an accurate guide to propose new physics beyond the Standard Model and argued that supersymmetry may be realized in a different fashion that preserved gauge coupling unification and has a dark matter candidate. In June 2004 Gian Giudice and Andrea Romanino argued from a general point of view that if one wants gauge coupling unification and a dark matter candidate, that split supersymmetry is one amongst a few theories that exists.

The new light (~TeV) particles in Split Supersymmetry (beyond the Standard Models particles) are

The Lagrangian for Split Supersymmetry is constrained from the existence of high energy supersymmetry. There are five couplings in Split Supersymmetry: the Higgs quartic coupling and four Yukawa couplings between the Higgsinos, Higgs and gauginos. The couplings are set by one parameter, , at the scale where the supersymmetric scalars decouple. Beneath the supersymmetry breaking scale, these five couplings evolve through the renormalization group equation down to the TeV scale. At a future Linear collider, these couplings could be measured at the 1% level and then renormalization group evolved up to high energies to show that the theory is supersymmetric at an exceedingly high scale.


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.


In particle physics, a superpartner (also sparticle) is a class of hypothetical elementary particles. Supersymmetry is one of the synergistic theories in current high-energy physics that predicts the existence of these “shadow" particles.When considering extensions of the Standard Model, the s- prefix from sparticle is used to form names of superpartners of the Standard Model fermions (sfermions), e.g. the stop squark. The superpartners of Standard Model bosons have an -ino (bosinos) appended to their name, e.g. gluino, the set of all gauge superpartners are called the gauginos.

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