Futaki invariant for Fedosov star products

We study obstructions to the existence of closed Fedosov star products on a
given Kähler manifold (M, omega, J). In our previous paper [11], we proved that if the
Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of
Connes-Flato-Sternheimer [4]) Fedosov’s star product then it is a zero of a moment
map μ on the space of symplectic connections. By analogy with the Futaki invariant
obstructing the existence of cscK metrics, we build an obstruction for the existence
of zero of μ and hence for the existence of closed Fedosov’s star product on a Kähler
manifold.