Scattering in Instanton Backgrounds

TL;DR

This paper computes one-loop gluon amplitudes in an SU(Nc) gauge theory with fermions in an instanton background, revealing modifications to soft theorems and the structure of amplitudes due to instanton effects.

Contribution

It introduces a method to evaluate one-loop all-plus gluon amplitudes with fermions in an instanton background, connecting anomaly cancellation to amplitude structure.

Findings

Amplitude has a Parke-Taylor form multiplied by the Fourier transform of instanton density.

Instanton modifies soft gluon and photon theorems, affecting Kac-Moody symmetry.

Results have implications for amplitudes with dynamical instantons.

Abstract

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.