  We study loops of symplectic diffeomorphisms of closed symplectic manifolds.
Our main result, which is valid for a large class of symplectic manifolds,
shows that the flux of a symplectic loop vanishes whenever its orbits are
contractible. As a consequence, we obtain a new vanishing result for the flux
group and new instances where the presence of a fixed point of a symplectic
circle action is a sufficient condition for it to be Hamiltonian. We also
obtain applications to symplectic torsion, more precisely, non-trivial elements
of $\mathrm{Symp}_{0}(M,\omega)$ that have finite order.
