supersymmetry
The Standard Model splits the world in two: fermions, the particles of matter that refuse to share a state, and bosons, the particles of force that pile up happily together. Supersymmetry proposes that this divide is not fundamental but a broken symmetry, that every fermion has a boson partner and every boson has a fermion partner, related by a symmetry that swaps the two families. It is the most studied idea for physics beyond the Standard Model, elegant enough to have dominated theoretical particle physics for decades, yet so far entirely unconfirmed by experiment.
Supersymmetry, often abbreviated SUSY, is a proposed symmetry relating particles of spin differing by one-half, fermions and bosons. Every known particle would have a superpartner: the electron a scalar 'selectron,' the quarks 'squarks,' the photon a 'photino,' and so on, with partners named by adding an s to fermions or -ino to bosons. Mathematically it extends the spacetime symmetries of relativity (the Poincare group) by generators that turn a fermion into a boson and back, the unique consistent way to do so. If the symmetry were exact, superpartners would have equal mass to their partners; since no such partners have been seen, supersymmetry must be broken, pushing the superpartner masses higher, presumably to the TeV scale or beyond.
Why take it seriously? Supersymmetry offers three prizes at once. It tames the hierarchy problem, the puzzle of why the Higgs mass is not dragged up to enormous values by quantum corrections, because the contributions of a particle and its superpartner cancel. It provides a natural dark matter candidate: the lightest, stable superpartner. And it makes the three Standard Model force couplings meet almost exactly at a single high energy, hinting at grand unification. The honest problem is that after extensive searches at the Large Hadron Collider, no superpartners have appeared, ruling out the simplest versions and pushing the rest into increasingly fine-tuned corners. Supersymmetry remains a beautiful, motivated, and unconfirmed hypothesis.
In the simplest supersymmetric models the lightest superpartner, often a neutral particle called the neutralino, would be stable and interact only weakly, making it an almost perfect fit for the invisible dark matter that outweighs ordinary matter across the cosmos, which is why so many dark-matter searches were designed to find it.
The lightest superpartner is supersymmetry's most tantalizing offer: a ready-made dark matter particle.
Supersymmetry is a well-motivated hypothesis, not an established fact; the LHC has found no superpartners so far, excluding the simplest models and constraining the rest, so its status remains an open experimental question.