Supersymmetry

[2] If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics.

A. Golfand and E. P. Likhtman (also in 1971), and D. V. Volkov and V. P. Akulov (1972),[15][16][17] independently rediscovered supersymmetry in the context of quantum field theory, a radically new type of symmetry of spacetime and fundamental fields, which establishes a relationship between elementary particles of different quantum nature, bosons and fermions, and unifies spacetime and internal symmetries of microscopic phenomena.

Supersymmetry with a consistent Lie-algebraic graded structure on which the Gervais−Sakita rediscovery was based directly first arose in 1971 in the context of an early version of string theory by Pierre Ramond, John H. Schwarz and André Neveu.

[24][25] The term supergauge was in turn coined by Neveu and Schwarz in 1971 when they devised supersymmetry in the context of string theory.

In 1971 Golfand and Likhtman were the first to show that the Poincaré algebra can be extended through introduction of four anticommuting spinor generators (in four dimensions), which later became known as supercharges.

In 1975, the Haag–Łopuszański–Sohnius theorem analyzed all possible superalgebras in the general form, including those with an extended number of the supergenerators and central charges.

This extended super-Poincaré algebra paved the way for obtaining a very large and important class of supersymmetric field theories.

In 2021, supersymmetric quantum mechanics was applied to option pricing and the analysis of markets in finance,[27] and to financial networks.

[dubious – discuss][28] In quantum field theory, supersymmetry is motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies.

Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem, which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories with very general assumptions.

[30][31] The realization of this effective supersymmetry is readily explained in quark–diquark models: Because two different color charges close together (e.g., blue and red) appear under coarse resolution as the corresponding anti-color (e.g. anti-green), a diquark cluster viewed with coarse resolution (i.e., at the energy-momentum scale used to study hadron structure) effectively appears as an antiquark.

The use of the supersymmetry method provides a mathematical rigorous alternative to the replica trick, but only in non-interacting systems, which attempts to address the so-called 'problem of the denominator' under disorder averaging.

[34] In 2013, integrated optics was found[35] to provide a fertile ground on which certain ramifications of SUSY can be explored in readily-accessible laboratory settings.

In this manner, a new class of functional optical structures with possible applications in phase matching, mode conversion[36] and space-division multiplexing becomes possible.

[37] All stochastic (partial) differential equations, the models for all types of continuous time dynamical systems, possess topological supersymmetry.

When the topological supersymmetry is broken spontaneously, this property is violated in the limit of the infinitely long temporal evolution and the model can be said to exhibit (the stochastic generalization of) the butterfly effect.

From a more general perspective, spontaneous breakdown of the topological supersymmetry is the theoretical essence of the ubiquitous dynamical phenomenon variously known as chaos, turbulence, self-organized criticality etc.

The Goldstone theorem explains the associated emergence of the long-range dynamical behavior that manifests itself as ⁠1/f⁠ noise, butterfly effect, and the scale-free statistics of sudden (instantonic) processes, such as earthquakes, neuroavalanches, and solar flares, known as the Zipf's law and the Richter scale.

[44][45] Despite the null results for supersymmetry at the LHC so far, some particle physicists have nevertheless moved to string theory in order to resolve the naturalness crisis for certain supersymmetric extensions of the Standard Model.

[46] According to the particle physicists, there exists a concept of "stringy naturalness" in string theory,[47] where the string theory landscape could have a power law statistical pull on soft SUSY breaking terms to large values (depending on the number of hidden sector SUSY breaking fields contributing to the soft terms).

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.

Another motivation for the Minimal Supersymmetric Standard Model comes from grand unification, the idea that the gauge symmetry groups should unify at high-energy.

In particular, the renormalization group evolution of the three gauge coupling constants of the Standard Model is somewhat sensitive to the present particle content of the theory.

Prior to the beginning of the LHC, in 2009, fits of available data to CMSSM and NUHM1 indicated that squarks and gluinos were most likely to have masses in the 500 to 800 GeV range, though values as high as 2.5 TeV were allowed with low probabilities.

[64] The first runs of the LHC surpassed existing experimental limits from the Large Electron–Positron Collider and Tevatron and partially excluded the aforementioned expected ranges.

The current best limit for the electron's EDM has already reached a sensitivity to rule out so called 'naive' versions of supersymmetric extensions of the Standard Model.

[68] Research in the late 2010s and early 2020s from experimental data on the cosmological constant, LIGO noise, and pulsar timing, suggests it's very unlikely that there are any new particles with masses much higher than those which can be found in the standard model or the LHC.

[74][47][48][50] Former enthusiastic supporter Mikhail Shifman went as far as urging the theoretical community to search for new ideas and accept that supersymmetry was a failed theory in particle physics.

[75] However, some researchers suggested that this "naturalness" crisis was premature because various calculations were too optimistic about the limits of masses which would allow a supersymmetric extension of the Standard Model as a solution.

It is not known how to make massless fields with spin greater than two interact, so the maximal number of supersymmetry generators considered is 32.