  Over any field of positive characteristic we construct 2-CY-tilted algebras
that are not Jacobian algebras of quivers with potentials. As a remedy, we
propose an extension of the notion of a potential, called hyperpotential, that
allows to prove that certain algebras defined over fields of positive
characteristic are 2-CY-tilted even if they do not arise from potentials.
  In another direction, we compute the fractionally Calabi-Yau dimensions of
certain orbit categories of fractionally CY triangulated categories. As an
application, we construct a cluster category of type $G_2$.
