ALGEBRA
SPECTRUM
SOFT BREAKING
SUSY POTENTIAL
Supersymmetry is the unique extension of spacetime symmetry relating bosons and fermions: Q_α|boson⟩ = |fermion⟩.
The SUSY algebra: {Q_α, Q̄_β̇} = 2σ^μ_αβ̇ P_μ — supercharges anti-commute to the momentum operator.
SUSY breaking: if ⟨F⟩ ≠ 0 (F-term breaking) or ⟨D⟩ ≠ 0 (D-term breaking), the vacuum energy E = |⟨F⟩|² > 0, and SUSY is broken.
Soft terms from the hidden sector give mass splittings m² ~ F²/M²_Pl (gravity mediation). LHC constraints push M_SUSY ≳ 1-2 TeV; the Higgs at 125 GeV requires significant tuning in simple MSSM.