  Form factors of self-dual gauge theory are equal to correlators of an
(extended) celestial chiral algebra. This suggests that these form factors can
be computed using the "bootstrap" method familiar from 2d CFTs. The method can
also be applied to certain QCD amplitudes, which are built from form-factors of
self-dual gauge theory.
  In this paper this bootstrap method is applied to compute two-loop all-plus
QCD amplitudes, for $SU(N)$ gauge theory with certain special matter conent. A
closed formula is presented for all single-trace amplitudes.
