| supersymmetry | |
|---|---|
| Name | Supersymmetry |
| Field | Theoretical physics |
| Introduced | 1971 |
| Proponents | Julius Wess and Bruno Zumino |
| Related | Quantum field theory, String theory |
supersymmetry
Supersymmetry is a proposed symmetry relating bosons and fermions in quantum field theories. It extends the Poincaré group by introducing fermionic generators that transform bosonic states into fermionic ones and vice versa, with implications for particle spectra, hierarchy problems, and unification. Supersymmetry matters in Quantum Physics and high-energy physics because it offers mechanisms for stabilizing the Higgs boson mass, providing dark matter candidates, and connecting to String theory and Quantum gravity.
Supersymmetry (SUSY) was first formulated in the early 1970s by Dmitry Volkov, Vladimir Akulov, Julius Wess and Bruno Zumino and later developed in the context of N=1 supersymmetry, extended SUSY, and higher-dimensional models. Motivations include solving the hierarchy problem by canceling quadratic divergences in radiative corrections to the Higgs field, providing weakly interacting massive particle (WIMP) dark matter candidates such as the neutralino, and improving gauge coupling unification in the MSSM and its extensions. SUSY also constrains quantum corrections via nonrenormalization theorems and relates to algebraic structures in representation theory.
The defining structure is the supersymmetry algebra: an extension of the Poincaré algebra by spinor generators Qα satisfying anticommutation relations {Qα, Q̄β̇} ∼ (σμ)αβ̇ Pμ plus possible central charges. Representations are described by supermultiplets such as chiral multiplets and vector multiplets in four dimensions with N supersymmetries (e.g., N=1, N=2, N=4). Mathematical tools include Grassmann variables, supermanifold theory, and Lie superalgebra classification. Techniques from algebraic geometry and cohomology appear in the analysis of BPS states, while the concept of holomorphy underlies nonrenormalization theorems like those proven by Seiberg.
Supersymmetric quantum field theories (SQFTs) generalize Quantum field theory by pairing fields into superfields and encoding interactions in superspace. Notable models include the Wess–Zumino model, the MSSM, supersymmetric gauge theories like supersymmetric Yang–Mills theory, and conformal examples such as N=4 supersymmetric Yang–Mills theory. Supersymmetric renormalization group flows, anomaly matching (e.g., by 't Hooft), and dualities such as Seiberg duality constrain low-energy dynamics. Exact results in SQFT have been obtained using localization, the Seiberg–Witten solution for N=2 theories, and the AdS/CFT correspondence connecting N=4 SYM with Type IIB string theory on AdS5 × S5.
Phenomenological implementations map supersymmetric spectra to collider and astroparticle signals. The MSSM predicts superpartners: squarks, sleptons, gluinos, charginos, and neutralinos; the lightest supersymmetric particle (LSP) is often stable under R-parity and is a dark matter candidate. Experimental searches at the Large Hadron Collider (LHC), including the ATLAS and CMS experiments, set limits on superpartner masses and constrained simplified models used by the Particle Data Group. Indirect probes include precision electroweak measurements, flavor physics constraints from experiments like LHCb and Belle II, and dark matter searches by XENON and Fermi Gamma-ray Space Telescope. No conclusive evidence has been observed; null results motivate models with compressed spectra, heavy scalars, or split supersymmetry scenarios.
Supersymmetry plays a central role in constructing consistent theories of quantum gravity. Supergravity arises from localizing global SUSY and yields theories such as eleven-dimensional 11-dimensional supergravity which relate to M-theory. In String theory, worldsheet supersymmetry leads to superstring theories (Type I, Type IIA, Type IIB, heterotic SO(32) and E8×E8) that require SUSY for anomaly cancellation and stability. SUSY stabilizes vacua, facilitates dualities (T-duality, S-duality), and supports extended objects like D-branes. Phenomenological compactifications (e.g., on Calabi–Yau manifolds) produce low-energy SUSY effective actions that connect to particle physics.
Supersymmetry must be broken in nature; spontaneous and explicit breaking mechanisms are studied to produce realistic spectra. Common mediation mechanisms include gravity mediation, gauge mediation, and anomaly mediation. Models such as the MSSM require soft SUSY-breaking terms to avoid reintroducing quadratic divergences. Alternative frameworks include split supersymmetry, high-scale supersymmetry, and models with Dirac gauginos or compressed spectra. Model builders confront constraints from electroweak symmetry breaking, flavor-changing neutral currents (FCNCs), CP violation, and cosmological considerations like moduli stabilization and the cosmological gravitino problem.
Computational tools and methods for SUSY include symbolic manipulation of superspace and component actions, lattice approaches for lower-dimensional supersymmetric systems, and numerical scans of parameter spaces with programs like SOFTSUSY, SPheno, Suspect, MadGraph and Pythia for collider simulation. Exact techniques include supersymmetric localization, integrability in planar N=4 SYM, and bootstrap methods. Applications extend to condensed matter analogues (supersymmetric quantum mechanics), black hole microstate counting via BPS states and the Strominger–Vafa calculation, and insights into nonperturbative dynamics relevant to both particle physics and mathematical physics.
Category:Theoretical physics Category:Quantum field theory Category:Particle physics