The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity

TL;DR

This paper explores how color-kinematics duality constrains the high-energy behavior of deformed gauge theories and their implications for supergravity and string theory, revealing a trade-off with locality.

Contribution

It demonstrates that certain higher-derivative deformations cannot be color-dual without additional counterterms and links these findings to string-inspired theories via explicit calculations.

Findings

Higher-derivative $F^3$ deformations are incompatible with color-kinematics duality without extra counterterms.

Resummation suggests a connection to the $(DF)^2+YM$ theory and string theory expansions.

Double-copy constructions lead to higher-derivative gravity theories including string theory limits.

Abstract

We find that the duality between color and kinematics can be used to inform the high energy behavior of effective field theories. Namely, we demonstrate that the massless gauge theory of Yang-Mills deformed by a higher-derivative $F^3$ operator cannot be tree-level color-dual while consistently factorizing without a tower of additional four-point counterterms with rigidly fixed Wilson coefficients that reaches to the ultraviolet (UV). We find through explicit calculation a suggestive resummation, namely that their amplitudes are consistent with the $\alpha'$ expansion of those generated by the $(DF)^2+\text{YM}$ theory, a known color-dual theory where the $F^2$ term has been given a mass squared proportional to $1 / \alpha'$. As a result, considering consistent double-copy construction as a physical principle implies that an $F^3$-based color-dual resolution of the UV divergence in $\mathcal{N}=4$ supergravity comes at the cost of field-theoretic locality. Similarly, when double-copying $F^3$ with itself, double-copy consistency lifts $R^3$ gravity to a family of gravity theories with an all-order tower of higher-derivative corrections, which includes the closed bosonic string as a standard adjoint-type double-copy.