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We study lattice QCD with $N_f=2$ Wilson fermions at nonzero imaginarychemical potential and nonzero temperature. We relate the Roberge - Weiss phasetransition to the properties of dyons which are constituents of the KvBLLcalorons. We present numerical evidence that the characteristic features of thespectral gap of the overlap Dirac operator as function of an angle modifyingthe boundary condition are determined by the $Z_3$ sector of the respectiveimaginary chemical potential. We then demonstrate that dyon excitations inthermal configurations could be responsible (in line with perturbativeexcitations) for these phenomena.

Dyons and Roberge - Weiss transition in lattice QCD