Kirby killing property
= Kirby killing property
{c}
{title2=$K_\Omega(x)=\mathcal D\delta_{x1}$}
In a <modular tensor category>, a loop with the <normalized Kirby color> encircling a charge-$x$ strand projects onto the <vacuum anyon> charge and multiplies it by $\mathcal D$. Indeed, the encircling scalar is $\mathcal D^{-1}\sum_a d_aS_{ax}/S_{1x}$, which equals $\mathcal D\delta_{x1}$ by <unitary matrix> orthogonality for the <modular S-matrix>.