Two-loop QCD Amplitudes from the Chiral Algebra Bootstrap

TL;DR

This paper demonstrates how the chiral algebra bootstrap approach can simplify the calculation of two-loop QCD amplitudes, providing new results for all-plus-helicity configurations using form factors and supersymmetry identities.

Contribution

It introduces a novel method leveraging chiral algebra bootstrap to compute two-loop QCD amplitudes, reducing complexity and deriving previously unknown partial amplitudes.

Findings

Derived a new n-gluon partial amplitude at two loops for all-plus helicity.

Showed that full-color two-loop amplitudes can be obtained from form factors and lower-order amplitudes.

Demonstrated the bootstrap's effectiveness in simplifying complex amplitude calculations.

Abstract

We show that the chiral algebra bootstrap, which computes form factors of twistorial theories, can help determine two-loop amplitudes in massless QCD. We give an $n$-gluon result for a previously unknown partial amplitude of the two-loop all-plus-helicity QCD amplitude by utilizing supersymmetry Ward identities and known chiral algebra bootstrap results. We then show that the full-color two-loop $n$-gluon amplitude of QCD with $n_f$ quark flavors can be obtained from certain two-loop form factors of twistorial theories and one-loop and tree-level amplitudes. Chiral algebra bootstrap results exist for these form factors when all gluons have positive helicities. Hence, the bootstrap simplifies the computation of these two-loop amplitudes by one loop level.