Global wellposedness for the energy-critical Zakharov system below the ground state

The Cauchy problem for the Zakharov system in energy-critical dimension $d=4$ is considered. We prove that global well-posedness holds full (non-radial) energy space any initial data with and wave mass below ground state threshold. result based on a Strichartz estimate Schr\"odinger equation potential. More precisely, proved to hold uniformly potential solving free constraint. key new ingredient bilinear (adjoint) Fourier restriction solutions of inhomogeneous forcing dual endpoint spaces.