= Spin bound for massless supermultiplets
{title2=$\mathcal N\le4s$}
In four-dimensional <supersymmetry>, a finite-<helicity> <massless supermultiplet> has <helicity> interval of width $\mathcal N/2$. If every state obeys $|h|\le s$, that interval fits inside one of width $2s$, giving $\mathcal N\le4s$. The bounds $4$ for $s=1$ and $8$ for $s=2$ are attained by the <four-dimensional N=4 super Yang-Mills theory> <vector multiplet> and the <four-dimensional N=8 supergravity> <supergravity multiplet>. Spin bounds alone do not prove that an arbitrary action is renormalizable.
Back to article page
