Simple encoding of higher derivative gauge and gravity counterterms

TL;DR

This paper presents a simplified method to incorporate higher derivative operators in gauge and gravity theories using scalar theory corrections and the double-copy approach, revealing minimal building blocks for four-point amplitudes.

Contribution

It introduces a novel way to encode higher derivative operators in supersymmetric theories through simpler scalar theory corrections and minimal building blocks, streamlining amplitude predictions.

Findings

Higher derivative operators can be absorbed into scalar theory corrections.

A small set of building blocks suffices for four-point amplitude predictions.

The approach reproduces string theory amplitude structures.

Abstract

Invoking increasingly higher dimension operators to encode novel UV physics in effective gauge and gravity theories traditionally means working with increasingly more finicky and difficult expressions. We demonstrate that local higher derivative supersymmetric-compatible operators at four-points can be absorbed into simpler higher-derivative corrections to scalar theories, which generate the predictions of Yang-Mills and Gravity operators by suitable replacements of color-weights with color-dual kinematic weights as per Bern-Carrasco-Johansson double-copy. We exploit that Jacobi-satisfying representations can be composed out of other Jacobi-satisfying representations, and show that at four-points only a small number of building blocks are required to generate the predictions of higher-derivative operators. We find that this construction saturates the higher-derivative operators contributing to the four-point supersymmetric open and closed-string tree amplitudes, presenting a novel representation of the four-point supersymmetric open string making this structure manifest, as well as identifying the only four additional gauge-invariant building blocks required to saturate the four-point bosonic open string.