Topological susceptibility at zero and finite $T$ in $SU(3)$ Yang-Mills theory

We determine the topological susceptibility $\chi$ at $T=0$ in pure $SU(3)$ gauge theory and its behaviour at finite $T$ across the deconfining transition. We use an improved topological charge density operator. $\chi$ drops sharply by one order of magnitude at the deconfining temperature $T_c$.