Frankel's theorem in the symplectic category

We prove that if an -dimensional torus acts symplectically on a -dimensional symplectic manifold, then the action has a fixed point if and only if the action is Hamiltonian. One may regard it as a symplectic version of Frankel's theorem which says that a Kähler circle action has a fixed point if and only if it is Hamiltonian. The case of is the well-known theorem by McDuff.