= Solution
A <BPS state> \b[saturates a supersymmetry energy bound and is annihilated by some supercharges]. For a massive state with one relevant <central charge in supersymmetry>, normalize the <supersymmetry algebra> by $\{Q^A_\alpha,Q^B_\beta\}=2\epsilon_{\alpha\beta}\epsilon^{AB}Z$. In its rest frame, appropriate linear combinations of <supercharges> have anticommutators $2(M+|Z|)$ and $2(M-|Z|)$. Positivity therefore gives the <BPS bound in supersymmetry> $M\geq|Z|$. At equality, the latter combinations have zero norm and annihilate the state, producing a shortened <supermultiplet> and preserved <supersymmetry>. With the alternative convention omitting the factor $2$ in the central-charge anticommutator, the bound reads $M\geq|Z|/2$. The mass is tied to the charge, but this does not imply unconditional stability against decay as parameters vary.
Back to article page
