Single-trace current correlators for 2d models of 4d gluon scattering

Abstract: Correlators of affine Kac-Moody currents evaluate to a sum over multi-color-trace contributions. We present a `single-trace current system' defined on a genus 0 Riemann surface, whose correlators evaluate to precisely the single-trace term in the evaluation of a standard affine Kac-Moody at level 1. We demonstrate that using the single-trace current system in genus 0 Berkovits-Witten twistor string correlators gives pure $\mathcal{N} = 4$ super Yang-Mills tree amplitudes, and explain how this works both at the level of the string theory correlator and from the perspective of the effective field theory. We explain how using the single-trace current system in genus 0 correlators of the ambitwistor string gives pure Yang-Mills tree amplitudes, and briefly discuss a proposal to go to higher loops.