| supersymmetry | |
|---|---|
| Name | Supersymmetry |
| Caption | Conceptual depiction of boson–fermion symmetry |
| Field | Quantum field theory |
| Introduced | 1970s |
| Notable people | Pierre Ramond, Yuri Golfand, Evgeny Likhtman, Julius Wess, Bruno Zumino |
supersymmetry
Supersymmetry (often abbreviated SUSY) is a proposed symmetry relating bosons and fermions within Quantum field theory and particle physics. It postulates that each particle of a given spin has a superpartner differing by half a unit of spin, addressing theoretical issues such as the hierarchy problem and providing candidates for dark matter. Supersymmetry matters in quantum physics because it extends the Poincaré group to include graded generators and yields powerful constraints on renormalization and model building.
Supersymmetry emerged in the late 1960s and early 1970s in independent work by Yuri Golfand and Evgeny Likhtman (Moscow), and by Pierre Ramond, Julius Wess, and Bruno Zumino in the West, building on concepts from S-matrix theory and early attempts at unifying internal and spacetime symmetries. The discovery that a graded extension of the Poincaré group could produce new conserved charges led to rapid development in supersymmetric quantum mechanics, supergravity, and later in string theory where supersymmetry plays a central role in stabilizing extra dimensions. Over decades, supersymmetry has influenced work at institutions like CERN, Fermilab, and SLAC National Accelerator Laboratory and shaped experimental programs at the Large Hadron Collider.
In Quantum field theory, supersymmetry is implemented via operators Qα that transform bosonic states into fermionic ones and satisfy anticommutation relations forming a superalgebra. The most common constructions are N=1 supersymmetry in four dimensions and extended cases (N>1). A supersymmetric Lagrangian mixes fields into supermultiplets, often expressed compactly with superspace and superfield formalisms developed by Wess and Zumino. Supersymmetry improves ultraviolet behavior of theories by canceling quadratic divergences, which is central to addressing the Higgs boson mass stabilization in the Standard Model context.
Supersymmetric models predict superpartners: scalar partners for Standard Model fermions (sfermions) and fermionic partners for bosons (gauginos, higgsinos). Notable multiplets include the chiral (or matter) multiplet and the vector (or gauge) multiplet. In minimal constructions such as the Minimal Supersymmetric Standard Model (MSSM) each known particle acquires a superpartner: gluino for the gluon, squarks for quarks, sleptons for leptons, and the neutralino and chargino mixtures arising from higgsinos and gauginos. Mechanisms of supersymmetry breaking, e.g., soft SUSY breaking, gravity mediation, and gauge mediation, determine masses and phenomenology of superpartners.
Supersymmetry facilitates gauge coupling unification by altering the renormalization group running of couplings, improving grand unification in models based on groups such as SU(5), SO(10), and E8. Supersymmetric extensions of gravity, notably supergravity, combine SUSY with the Einstein field equations and provide candidate low-energy limits of string theory frameworks like heterotic string theory and type II string theory. The AdS/CFT correspondence and developments in M-theory rely heavily on supersymmetric constructions, which provide controlled settings to study nonperturbative quantum gravity and black hole microstates (e.g., work by Juan Maldacena).
Experimental searches for supersymmetry have been a major priority at colliders and in astroparticle experiments. The Large Hadron Collider experiments ATLAS and CMS have set stringent limits on superpartner masses, excluding large regions of parameter space of the MSSM and simplified models. Indirect searches involve precision observables such as the anomalous magnetic moment of the muon, rare decays measured by LHCb and Belle II, and electroweak precision tests. Dark matter direct-detection experiments like XENON, LUX-ZEPLIN, and PandaX search for scattering of putative supersymmetric dark matter (often the lightest neutralino). Non-observation at expected scales has motivated alternative scenarios: split supersymmetry, high-scale SUSY, and compressed spectra.
Mathematically, supersymmetry is encoded in Lie superalgebras and graded geometry. The structure of supersymmetric theories uses Clifford algebra representations, spinor modules, and cohomological methods. Tools such as supersymmetric index theorems, localization techniques (e.g., Pestun's localization), and topological twists connect SUSY field theories to subjects in pure mathematics like algebraic geometry and representation theory. Important named mathematical results include the classification of simple superalgebras by Victor Kac and applications of supersymmetric quantum mechanics to Morse theory pioneered by Edward Witten.
Supersymmetry offers natural dark matter candidates, notably the lightest neutralino in R-parity conserving models, and the gravitino in scenarios with very weakly interacting particles. SUSY affects early-universe cosmology through moduli stabilization, reheating, baryogenesis mechanisms such as electroweak baryogenesis in extended Higgs sectors, and the cosmological moduli problem. Cosmological constraints from the cosmic microwave background measured by Planck and large-scale structure surveys constrain SUSY parameter space and guide model-building efforts that aim to preserve both theoretical virtues and observational concordance.