This is the second of a series of two papers devoted to the partition
function realization of Wilson surfaces in strict higher gauge theory. A higher
2–dimensional counterpart of the topological coadjoint orbit quantum
mechanical model computing Wilson lines is presented based on the derived
geometric framework, which has shown its usefulness in 4–dimensional higher
Chern–Simons theory.
Its symmetries are described. Its quantization is analyzed in the functional
integral framework. Strong evidence is provided that the model does indeed
underlie the partition function realization of Wilson surfaces. The emergence
of the vanishing fake curvature condition is explained and homotopy invariance
for a flat higher gauge field is shown. The model’s Hamiltonian formulation is
further furnished highlighting the model’s close relationship to the derived
Kirillov-Kostant-Souriau theory developed in the companion paper.
