Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators

TL;DR

The paper probes whether color-kinematics duality and the double-copy construction survive deformations of Yang–Mills by higher-dimension operators. It demonstrates that a single F^3 insertion yields CK-dual gauge-theory amplitudes whose gravity double-copy reproduces R^3-like corrections together with dilaton/axion exchange, aligning with the field-theory limit of KLT relations. For higher-dimension F^4-type operators, the typical color structures either obstruct duality or require delicate combinations (e.g., with (F^3)^2) to reflect string-theory differences; intriguingly, a specific O() term in the superstring effective action exhibits CK duality up to six gluons. Overall, CK duality and double-copy extend beyond renormalizable YM, revealing a deep link to string-theory amplitudes, though many higher-dimension cases challenge duality, guiding future investigations into generalized dualities and their string-theoretic underpinnings.

Abstract

We investigate color-kinematics duality for gauge-theory amplitudes produced by the pure nonabelian Yang-Mills action deformed by higher-dimension operators. For the operator denoted by F^3, the product of three field strengths, the existence of color-kinematic dual representations follows from string-theory monodromy relations. We provide explicit dual representations, and show how the double-copy construction of gravity amplitudes based on them is consistent with the Kawai-Lewellen-Tye relations. It leads to the amplitudes produced by Einstein gravity coupled to a dilaton field phi, and deformed by operators of the form phi R^2 and R^3. For operators with higher dimensions than F^3, such as F^4-type operators appearing at the next order in the low-energy expansion of bosonic and superstring theory, the situation is more complex. The color structure of some of the F^4 operators is incompatible with a simple color-kinematics duality based on structure constants f^{abc}, but even the color-compatible F^4 operators do not admit the duality. In contrast, the next term in the alpha-prime expansion of the superstring effective action --- a particular linear combination of D^2 F^4 and F^5-type operators --- does admit the duality, at least for amplitudes with up to six external gluons.

Figures (3)

• Figure 1: The three cubic graphs at the four-point level.
• Figure 2: The $m$-gluon amplitudes produced by the operator $F^3$, where $m_+$ and $m_-$ are the numbers of positive- and negative-helicity gluons, respectively. The left tower (red circles) of amplitudes is the self-dual sector, produced by $F^3_{ SD}$. The right tower (green circles) is produced by the anti-self-dual operator $F^3_{ ASD}$. For MHV ($\overline{\hbox{MHV}}$) amplitudes with exactly three negative (positive) helicities, the circles are filled. The figure is from ref. DixonGloverKhoze.
• Figure 3: Next-to-MHV $F^3$ amplitudes are constructed by sewing together two MHV vertices, one for $F^3$ (white circle) and one for ordinary gauge theory (black dot). There are two distinct ways of distributing the four negative-helicity gluons, (a) and (b). The dotted lines indicate that an arbitrary number of positive-helicity gluons may be present.