Scattering in Instanton Backgrounds

In this letter we evaluate one-loop all-plus gluon amplitudes of $\mathrm{SU}(N_c)$ gauge theory with $N_f$ fundamental fermions in the presence of a flavour instanton background. Fermion zero modes are regulated with a chiral mass term. This computation is performed by cancelling a twistorial 't Hooft anomaly via the Green-Schwarz mechanism. We find that the trace-ordered amplitude has the form of a Parke-Taylor factor multiplied by the Fourier transform of the instanton density evaluated on the total momentum of the gluons. A background flavour instanton modifies the leading soft gluon and photon theorem, generating a level equal to twice the instanton charge in the soft Kac-Moody symmetry. We discuss the implications of our results for amplitudes in the presence of dynamical instantons.