Uniqueness of MHV Gravity Amplitudes

TL;DR

This paper explores the unique mathematical structure of MHV gravity amplitudes at tree level, highlighting their distinctive properties and proposing a conjecture about the uniqueness of their numerators, supported by computational evidence.

Contribution

It introduces a conjecture on the uniqueness of the numerator in MHV gravity amplitudes and offers a new mathematical approach with computational validation.

Findings

Gravity amplitudes lack logarithmic singularities.

Numerators of these amplitudes have interesting zeroes.

Computational evidence supports the conjecture in specific cases.

Abstract

We investigate MHV tree-level gravity amplitudes as defined on the spinor-helicity variety. Unlike their gluon counterparts, the gravity amplitudes do not have logarithmic singularities and do not admit Amplituhedron-like construction. Importantly, they are not determined just by their singularities, but rather their numerators have interesting zeroes. We make a conjecture about the uniqueness of the numerator and explore this feature from a more mathematical perspective. This leads us to a new approach for examining adjoints. We outline steps of our proposed proof and provide computational evidence for its validity in specific cases.