symmetry between bosons and fermions in certain physical systems

In particle physics, supersymmetry (SUSY) is a theory that links gravity with the other fundamental forces of nature by proposing a relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin. A type of spacetime symmetry, supersymmetry is a possible candidate for undiscovered particle physics, and seen 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 would resolve major hierarchy problems within gauge theory, by guaranteeing that quadratic divergences of all orders will cancel out in perturbation theory.


  • If the Standard Model describes the world successfully, how can there be physics beyond it, such as supersymmetry? There are two reasons. First, the Standard Model does not explain aspects of the study of the large-scale universe, cosmology. For example, the Standard Model cannot explain why the universe is made of matter and not antimatter, nor can it explain what constitutes the dark matter of the universe. Supersymmetry suggests explanations for both of these mysteries. Second, the boundaries of physics have been changing. Now scientists ask not only how the world works (which the Standard Model answers) but why it works that way (which the Standard Model cannot answer). Einstein asked "why" earlier in the twentieth century, but only in the past decade or so have the "why" questions become normal scientific research in particle physics rather than philosophical afterthoughts.
  • It would not be an exaggeration to say that today supersymmetry dominates theoretical high energy physics. Many believe it will play the same revolutionary role in the physics of the 21st as special and general relativity did in the physics of the 20th century. This belief is based on aesthetical appeal, on indirect evidence, and the fact that no theoretical alternative is in sight.
  • The mathematical consistency of string theory depends crucially on supersymmetry, and it is very hard to find consistent solutions (quantum vacua) that do not preserve at least a portion of this supersymmetry. This prediction of string theory differs from the other two (general relativity and gauge theories) in that it really is a prediction. It is a generic feature of string theory that has not yet been discovered experimentally.
  • If dark matter is truly made of the lightest SUSY particle, then experiments designed to see it such as CDMS, XENON, Edelweiss and more should have detected it. Furthermore, SUSY dark matter should annihilate in a very particular way which hasn't been seen. Constraints on WIMP dark matter are quite severe, experimentally. The lowest curve rules out WIMP (weakly interacting massive particle) cross-sections and dark matter masses for anything located above it. This means that most models for SUSY dark matter are no longer viable.
  • Of the proposed extensions to the Standard Model, supersymmetry (SUSY) has remained among the most popular for decades. It provides exactly the needed compensation to stabilize the Higgs mass, while additionally providing an ideal candidate for dark matter with a stable weakly interacting lightest supersymmetric particle (LSP).
  • The concept of naturalness is usually cited as the underlying motivation for supersymmetry. We will challenge that concept, and in any case need to point out that there is nothing natural about the development of the theory itself. Its main success is its agility in dodging the facts. The dubious explanation of the convergence of the three scaling coupling constants into a single point can not be taken seriously. It is just another fit, using some of the many free parameters.
  • There is an infinite number of Lie groups that can be used to combine particles of the same spin in ordinary symmetry multiplets, but there are only eight kinds of supersymmetry in four spacetime dimensions, of which only one, the simplest, could be directly relevant to observed particles.
  • Steven Weinberg, "Preface". The Quantum Theory of Fields. vol. III. Cambridge University Press. 1995. p. xvi. 
  • Arkani-Hamed and Dimopoulos ... have even shown how it is possible to keep the good features of supersymmetry, such as a more accurate convergence of the SU(3) × SU(2) × U(1) couplings to a single value, and the presence of candidates for dark matter WIMPs. The idea of this “split supersymmetry” is that, although supersymmetry is broken at some very high energy, the gauginos and higgsinos are kept light by a chiral symmetry. [An additional discrete symmetry is needed to prevent lepton-number violation in higgsino-lepton mixing, and to keep the lightest supersymmetric particle stable.]
  • Supersymmetry is a subject of considerable interest among physicists and mathematicians. Not only is it fascinating in its own right, but there is a growing belief that it may play a fundamental role in particle physicis. This belief is based on an important result of Haag, Sohnius, and Lopuszanski, who proved that the supersymmetry algebra is the only graded Lie algebra of symmetries of the S-matrix consistent with relativistic quantum field theory.
  • Julius Wess and Jonathan Bagger: Supersymmetry and Supergravity: Revised and Expanded Edition. Princeton Series in Physics. 1992. ISBN 0-691-02530-4.  (p. 3)
  • The unification of forces, even if it were perfected, would leave us with two great kingdoms of particles, still not unified. Technically, these are the fermion and boson kingdoms. More poetically, we may call them the kingdoms of substance (fermions) and force (bosons).
    By postulating that the fundamental equations enjoy the property of supersymmetry, we heal the division of particles into separate kingdoms. Supersymmetry can be approached from several different angles, but perhaps the most appealing is to consider it as an expansion of space-time, to include quantum dimensions. The defining characteristic of quantum dimensions is that they are represented by coordinates that are Grassmann numbers (i.e., anticommuting numbers) rather than real numbers. Supersymmetry posits that the fundamental laws of physics remain invariant transformations that correspond to uniform motion in the quantum dimensions. Thus supersymmetry extends Galileo/Lorentz invariance.
  • Supersymmetry is an updating of special relativity to include fermionic as well as bosonic symmetries of spacetime. In developing relativity, Einstein assumed that the spacetime coordinates were bosonic; fermions had not yet been discovered! In supersymmetry the structure of spacetime is enriched by the presence of fermionic as well as bosonic coordinates.
  • … Supersymmetry … the virtues:
    * SUSY can make a “small” Higgs mass natural;
    • SUSY is part of a larger vision of physics, not just a technical solution;
    • the measured value of sin2θW favors SUSY GUT’s;
    • SUSY survives electroweak tests; and
    • the top quark mass has turned out to be heavy, as needed for electroweak symmetry breaking in the context of SUSY.
  • SUSY is a unique new symmetry that relates bosons to fermions, in a sense explaining why fermions exist. Relating bosons to fermions also makes it possible to explain the smallness of the Higgs mass, since we do know why the smallness of fermion masses can be natural. So that is at least the germ of how SUSY solves the fine-tuning problem.
    • Edward Witten, "Supersymmetry and other scenarios". Lepton and Photon Interactions at High Energies: Proceedings of the XXI International Symposium: Fermi National Accelerator Laboratory, USA, 11-16 August 2003. 19. World Scientific. 2004.  (For quote see pp. 2–3 of preprint.
  • ... I knew quantum field theory well enough to know that saying that the potential energy for the scalar field is zero is not a meaningful statement quantum mechanically. If it were, we would not have a gauge hierarchy problem in particle physics. ... with supersymmetry the mass renormalization (and even the full effective potential) of a scalar can be zero.
  • Edward Witten as quoted by Hirosi Ooguri in (2015). "Interview with Edward Witten". Notices of the AMS 62 (5): 491–506. (p. 483)
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