Please note that our editors may make some formatting changes or correct spelling or grammatical errors, and may also contact you if any clarifications are needed. Christine Sutton Learn More in these related Britannica articles: Quantum field theory , body of physical principles combining the elements of quantum mechanics with those of relativity to explain the behaviour of subatomic particles and their interactions via a variety of force fields.
Two examples of modern quantum field theories are quantum electrodynamics, describing the interaction of electrically charged particles…. Subatomic particle , any of various self-contained units of matter or energy that are the fundamental constituents of all matter. Subatomic particles include electrons, the negatively charged, almost massless particles that nevertheless account for most of the size of the atom, and they include the heavier building….
Supersymmetry , in particle physics, a symmetry between fermions subatomic particles with half-integer values of intrinsic angular momentum, or spin and bosons particles with integer values of spin. Supersymmetry is a complex mathematical framework based on the theory of group transformations that was developed beginning in the early s to understand…. Gravity , in mechanics, the universal force of attraction acting between all matter.
Supergravity
It is by far the weakest known force in nature and thus plays no role in determining the internal properties of everyday matter. On the other hand, through its long reach and universal action, it…. Fundamental interaction , in physics, any of the four basic forces—gravitational, electromagnetic, strong, and weak—that govern how objects or particles interact and how certain particles decay. All the known forces of nature can be traced to these fundamental interactions. The fundamental interactions are characterized on the basis of the following four…. Help us improve this article! Contact our editors with your feedback.
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Definition
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.
As in the nonsupersymmetric case, we have a Spin 3,1 principal bundle over M. We have an R 4 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.
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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 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 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.
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. In one version of SUGRA but certainly not the only one , we have the following constraints upon the torsion tensor:. R is a scalar valued chiral superfield derivable from the supervielbeins and spin connection.
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.
supergravity in nLab
This is called the Einstein frame. 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 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. 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. 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.
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December Learn how and when to remove this template message. Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons. String theory Loop quantum gravity Loop quantum cosmology Causal dynamical triangulation Causal fermion systems Causal sets Event symmetry Canonical quantum gravity Superfluid vacuum theory. Verlinde Witten Yau Zaslow. Annual Review of Nuclear and Particle Science.
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Strings History of string theory First superstring revolution Second superstring revolution String theory landscape. T-duality S-duality U-duality Montonen—Olive duality. Kaluza—Klein theory Compactification Why 10 dimensions? Supergravity Superspace Lie superalgebra Lie supergroup. Matrix theory Introduction to M-theory. Newton's law of universal gravitation History of gravitational theory. Classical theories of gravitation Quantum gravity Theory of everything. Kaluza—Klein theory Dilaton Supergravity. Bunch—Davies vacuum Hawking radiation Semiclassical gravity Unruh effect.
Bosonic string theory M-theory Supergravity Superstring theory. Loop quantum gravity Wheeler—DeWitt equation.