In particle physics, supersymmetry (SUSY) is a conjectured relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer-valued spin. A type of spacetime symmetry, supersymmetry is a possible candidate for undiscovered particle physics, and seen by some physicists as an elegant solution to many current problems in particle physics if confirmed correct, which could resolve various areas where current theories are believed to be incomplete. A supersymmetrical extension to the Standard Model could resolve major hierarchy problems within gauge theory, by guaranteeing that quadratic divergences of all orders will cancel out in perturbation theory.
In supersymmetry, each particle from one group would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. These superpartners would be new and undiscovered particles; for example, there would be a particle called a "selectron" (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly "unbroken" supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. Since it is expected to find these "superpartners" using present-day equipment, if supersymmetry exists then it consists of a spontaneously broken symmetry, allowing superpartners to differ in mass. Spontaneously broken supersymmetry could solve many problems in particle physics, including the hierarchy problem.
There is no experimental evidence that supersymmetry is correct, or whether or not other extensions to current models might be more accurate. It is only since around 2010 that particle accelerators specifically designed to study physics beyond the Standard Model have become operational (i.e. the Large Hadron Collider (LHC)), and it is not known where exactly to look, nor the energies required for a successful search.
The main reasons for supersymmetry being supported by some physicists is that the current theories are known to be incomplete and their limitations are well established, and supersymmetry could be an attractive solution to some of the major concerns.