UV consistency conditions for CHY integrands

We extend on-shell bootstrap methods from spacetime amplitudes to the worldsheet objects of the CHY formalism. We find that the integrands corresponding to tree-level non-linear sigma model, Yang-Mills and $(DF{)}^2$ theory are determined by demanding enhanced UV scaling under BCFW shifts. Back in spacetime, we also find that $(DF{)}^2$ theory is fixed by gauge invariance/UV scaling and simple locality assumptions.