Bootstrapping two-loop QCD amplitudes

TL;DR

This paper introduces a bootstrap approach inspired by 2D conformal field theory to compute two-loop all-plus QCD amplitudes, providing a new analytical method for these complex calculations.

Contribution

It applies the celestial chiral algebra bootstrap method to two-loop QCD amplitudes, deriving a closed formula for all single-trace amplitudes in specific gauge theories.

Findings

Derived a closed-form expression for two-loop all-plus QCD amplitudes

Extended bootstrap techniques from 2D CFT to QCD calculations

Validated the approach for $SU(N)$ gauge theories with special matter content

Abstract

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 content. A closed formula is presented for all single-trace amplitudes.