Simple encoding of higher derivative gauge and gravity counterterms

TL;DR

The paper investigates how higher-derivative UV physics in gauge and gravity theories can be encoded using adjoint-type color-kinematics duality and a minimal set of building blocks at four points. By applying a Jacobi-satisfying composition of color and kinematic weights, the authors derive three core color-building blocks and show they saturate all four-point single-trace higher-derivative corrections to Yang-Mills, which via the BCJ double-copy reproduce gravity corrections. They connect these field-theory blocks to string theory by matching to the low-energy expansion of open superstring amplitudes (via Z-theory) and open bosonic string amplitudes, identifying the four vector blocks needed for the bosonic case. The results point to a scalable approach for all-multiplicity and higher-loop corrections and illuminate the structure of color-kinematics duality in the presence of higher-derivative operators.

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.