In four spacetime dimensions, ''N'' = 8 supergravity, speculated by
Stephen Hawking
Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
, is the most
symmetric
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
quantum field theory which involves gravity and a finite number of fields. It can be found from a
dimensional reduction
Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in ''D'' spacetime dimensions can be redefined in a lower number of dimensions ''d'', by taking all the fields ...
of
eleven-dimensional supergravity
In supersymmetry, eleven-dimensional supergravity is the theory of supergravity in the highest number of dimensions allowed for a supersymmetric theory. It contains a graviton, a gravitino, and a 3-form gauge field, with their interactions unique ...
by making the size of seven of the dimensions go to zero. It has eight supersymmetries, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin −2. (The spin 2 graviton is the particle with the highest spin in this theory.) More supersymmetries would mean the particles would have
superpartner
In particle physics, a superpartner (also sparticle) is a class of hypothetical elementary particles predicted by supersymmetry, which, among other applications, is one of the well-studied ways to extend the Standard Model of high-energy physics.
...
s 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
Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
in his ''
Brief History of Time'' speculated that this theory could be the
theory of everything
A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a hypothetical singular, all-encompassing, coherent theoretical physics, theoretical framework of physics that fully explains and links togeth ...
. However, in later years this was abandoned in favour of
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
. There has been renewed interest in the 21st century, with the possibility that this theory may be finite.
Calculations
It has been found recently that the expansion of ''N'' = 8 supergravity in terms of
Feynman diagrams
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced ...
has shown that ''N'' = 8 supergravity is in some ways
a product of two
''N'' = 4 super Yang–Mills theories. This is written schematically as:
: N = 8 supergravity = (''N'' = 4 super Yang–Mills) × (''N'' = 4 super Yang–Mills)
This is not surprising, as ''N'' = 8 supergravity contains six independent representations of ''N'' = 4 super Yang–Mills.
Particle content
The theory contains 1
graviton
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with re ...
(spin 2), 8
gravitinos (spin 3/2), 28
vector boson
In particle physics, a vector boson is a boson whose spin equals one. Vector bosons that are also elementary particles are gauge bosons, the force carriers of fundamental interactions. Some composite particles are vector bosons, for instance any ...
s (spin 1), 56
fermions
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin ( spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and ...
(spin 1/2), 70
scalar fields
Scalar may refer to:
*Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers
*Scalar (physics), a physical quantity that can be described by a single element of a number field such a ...
(spin 0) where we do not distinguish particles with negative spin. These numbers are simple combinatorial numbers that come from
Pascal's triangle
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Bla ...
and also the number of ways of writing ''n'' as a sum of 8 nonnegative cubes
A173681.
One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the
orthogonal group
In mathematics, the orthogonal group in dimension , denoted , is the Group (mathematics), group of isometry, distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by ...
O(10).
For model building, it has been assumed that almost all the supersymmetries would be broken in nature, leaving just one supersymmetry (''N'' = 1), although nowadays because of the lack of evidence for ''N'' = 1 supersymmetry higher supersymmetries are now being considered such as ''N'' = 2.
Connection with superstring theory
''N'' = 8 supergravity can be viewed as the low-energy approximation of the type IIA or type IIB superstring with 6 of its dimensions compactified on a 6-torus. Equivalently, it may also be viewed as 11D M-theory with seven of its dimensions compactified on a 7-torus or 7-sphere.
See also
*
Pure 4D N = 1 supergravity
In supersymmetry, pure 4D \mathcal N=1 supergravity describes the simplest Four-dimensional space, four-dimensional supergravity, with a single supercharge and a supermultiplet containing a graviton and gravitino. The action (physics), action cons ...
*
Double copy theory
Double copy theory is a theory in theoretical physics, specifically in quantum gravity, that hypothesizes a perturbative duality between gauge theory and gravity. The theory says that scattering amplitudes in non-Abelian gauge theories can be f ...
References
{{DEFAULTSORT:N8 Supergravity
Supersymmetric quantum field theory
Theories of gravity