Color-Dual Fates of F

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 α^{'} expansion of those generated by the (DF)^{2}+YM theory, a known color-dual theory where the F^{2} term has been given a mass squared proportional to 1/α^{'}. 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 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.

Simple Encoding of Higher-Derivative Gauge and Gravity Counterterms.

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 find that the duality between color and kinematics provides a powerful tool towards drastic simplification. Local higher-derivative gauge and gravity operators at four points can be absorbed into simpler higher-derivative corrections to scalar theories, requiring only a small number of building blocks to generate gauge and gravity four-point amplitudes to all orders in mass dimension.

Perturbative quantum gravity as a double copy of gauge theory.

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.