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Supersymmetry is an integral part of string theory, a possible theory of everything. There are two types of string theory, supersymmetric string theory or superstring theory, and non-supersymmetric string theory. By definition of superstring theory, supersymmetry is required in superstring theory at some level.
To make progress on these problems, physicists developed supersymmetric quantum mechanics, an application of the supersymmetry superalgebra to quantum mechanics as opposed to quantum field theory. It was hoped that studying SUSY's consequences in this simpler setting would lead to new understanding; remarkably, the effort created new areas of ...
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics.
Supersymmetry extends the Standard Model by adding another class of symmetries to the Lagrangian. These symmetries exchange fermionic particles with bosonic ones. Such a symmetry predicts the existence of supersymmetric particles, abbreviated as sparticles, which include the sleptons, squarks, neutralinos and charginos.
In D=4 spacetime dimensions, N=4 is the maximal number of supersymmetries or supersymmetry charges. [1] SYM theory is a toy theory based on Yang–Mills theory; it does not model the real world, but it is useful because it can act as a proving ground for approaches for attacking problems in more complex theories. [2]
Without supersymmetry, a solution to the hierarchy problem has been proposed using just the Standard Model. The idea can be traced back to the fact that the term in the Higgs field that produces the uncontrolled quadratic correction upon renormalization is the quadratic one.
One approach to the representation theory of super Lie algebras is to restrict attention to representations in one space-time dimension and having supersymmetry generators, i.e., to (|) superalgebras. In that case, the defining algebraic relationship among the supersymmetry generators reduces to
Superspace is the coordinate space of a theory exhibiting supersymmetry.In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers.