Comments on the temperature dependence of the gauge topology

Recent efforts in lattice evaluation of the topological susceptibility had shown that at high temperatures it is given by well-separated instantons (even in QCD with light fermions, where those are highly suppressed). Recent development of the semiclassical theory suggest that below $T_{max}\sim 2.5T_c$, where Polyakov line has values between one and zero, the topology ensemble can be represented by a plasma of instanton constituents (called instanton-dyons or instanton-monopoles). It has been shown that such ensemble undergoes deconfinement and chiral transitions, semi-qualitatively reproducing the lattice results. There are ongoing efforts to locate them on the lattice, or use (flavor-dependent) periodicity phases of the deformed versions of QCD on the lattice and semiclassically, in order to test this theory. We here propose another possibly useful tool: the topological susceptibility of a sub-lattice.