supergravity

supergravity [¦sü·pər′grav·əd·ē]

(physics)

A supersymmetry which is used to unify general relativity and quantum theory; it is formed by adding to the Poincaré group, as a symmetry of space-time, four new generators that behave as spinors and vary as the square root of the translations.

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Supergravity

A theory that attempts to unify gravitation with the other fundamental interactions. The first, and only, completely successful unified theory was constructed by James Clerk Maxwell, in which the up-to-then unrelated electric and magnetic phenomena were unified in his electrodynamics. See Fundamental interactions, Maxwell's equations

Electroweak theory

The second stage of unification concerns the unification of electromagnetic and weak interactions, using Maxwell's theory as a guide. This was accomplished making use of the nonabelian gauge theories invented by C. N. Yang and R. L. Mills, and of spontaneous symmetry breaking. The symmetry of Maxwell's theory is very similar to spatial rotations about an axis, rotating the vector potentials while leaving the electric and magnetic fields unchanged. It is a local invariance because the rotations about a fixed axis can be made by different amounts at different points in space-time. Thus, Maxwell's theory is invariant under a one-parameter group of transformations U(1). In Yang-Mills theory this local invariance was generalized to theories with larger symmetry groups such as the three-dimensional rotation group SO(3) ≃ SU(2) which has three parameters. The number of parameters of the local symmetry (gauge) group is also equal to the number of 4-vector potentials in the gauge theory based on that group. A detailed analysis of weak and electromagnetic forces shows that their description requires four 4-vector potentials (gauge fields), so that the gauge group must be a four-parameter group. In fact, it is the product SU(2) · U(1). See Electroweak interaction, Symmetry breaking

Grand unified theories

In the third stage of unification, electroweak and strong forces are regarded as different components of a more general force which mediates the interactions of particles in a grand unified model. Strong forces are responsible for the interactions of hadrons and for keeping quarks confined inside hadrons. They are described by eight massless 4-vector potentials (gluons), the corresponding eight-parameter group being SU(3). This local symmetry is called color, and the corresponding theory quantum chromodynamics (QCD). The combination SU(3) · SU(2) · SU(1) has strong experimental support, and has come to be known as the standard model. Thus the gauge group of any grand unified model must include the standard model as a subsymmetry. The most dramatic prediction of these theories is the decay of protons. See Gluons, Grand unification theories, Proton, Quantum chromodynamics, Quarks, Standard model

Supersymmetry and supergravity theories

A still higher and more ambitious stage of unification deals with the possibility of combining grand unified and gravity theories into a superunified theory, also known as supergravity. To achieve this, use is made of the dual role played by local internal symmetry groups. On the one hand, they describe the behavior of forces. On the other hand, they classify the elementary particles (fields) of the theory into multiplets: spin-zero fields in one multiplet, spin-1/2 fields in another multiplet, and so forth, but never fermions and bosons in a single irreducible multiplet of internal symmetry. This last restriction used to be a major obstacle on the way to superunification. This is because, of all the elementary particles, only the quanta of the gravitational field (gravitons) have spin 2, so that a multiplet of elementary particles including the graviton must of necessity involve particles of different spin. But then by an internal symmetry transformation, which is by definition distinct from space-time (Lorentz) transformations, it is possible to “rotate” particles of different spin into one another, thus altering their space-time transformation properties. This apparent paradox can be circumvented if both the internal symmetry and Lorentz transformations are part of a larger (supersymmetric) transformation group which also includes the spin-changing transformations. The irreducible multiplets of such supergroups naturally contain both fermions and bosons. This is how supersymmetry makes its appearance in supergravity theories. See Graviton, Relativity, Supersymmetry, Symmetry laws (physics)

Effective theory

If supergravity models are regarded not as fundamental theories but as effective theories describing the low-energy behavior of superstring theories, it is possible to make a strong case for their usefulness. In that case, since supergravity is no longer a fundamental theory, it is no longer crucial that supergravity satisfy very stringent physical requirements such as renormalizability. In its role as an effective theory, supergravity has been used in a number of problems in particle physics. See Elementary particle, Quantum field theory, Superstring theory