Global shifted potentials for moduli stacks of sheaves on Calabi-Yau four-folds

abstract: It is shown that there are globally defined Lagrangian distributions on the stable loci of derived $\mathrm{Quot}$-stacks of coherent sheaves on Calabi--Yau four-folds. Dividing by these distributions produces perfectly obstructed smooth stacks with globally defined $-1$-shifted potentials, whose derived critical loci give back the stable loci of smooth stacks of sheaves in global Darboux form.