  We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian
five-dimensional gauge field theories with an $SU(1,3)$ conformal symmetry.
These actions have a Lagrange multiplier which imposes a novel
$\Omega$-deformed anti-self-dual gauge field constraint. Using a generalised 't
Hooft ansatz we find the constraint equation linearizes allowing us to
construct a wide class of explicit solutions. These include finite action
configurations that describe worldlines of anti-instantons which can be created
and annihilated. We also describe the dynamics on the constraint surface.
