Abstract
We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators α′F3 and α′2F4. Based on Berends-Giele recursions, the tensor structure of these amplitudes is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern-Carrasco-Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving α′R2 and α′2R3 operators.
Highlights
Recent investigations of scattering amplitudes in gauge theories and gravity revealed a wealth of mathematical structures and surprising connections between different theories
The organization of the Berends-Giele recursion (2.16) in terms of cubic-vertex diagrams as exemplified in figure 2 resonates with the BCJ duality between color and kinematics [2]: according to the BCJ duality, scattering amplitudes in non-abelian gauge theories can be represented in a manner such that color degrees of freedom can be freely interchanged with the kinematic variables
We have studied various representations for tree-level amplitudes of Ddimensional gauge theories with α F 3 + α 2F 4 deformations
Summary
Recent investigations of scattering amplitudes in gauge theories and gravity revealed a wealth of mathematical structures and surprising connections between different theories. By its close contact with Lagrangians, the construction in this work resonates with recent developments in scalar theories with color-kinematics duality and double-copy structures [42, 43]: for the color-kinematics duality of the non-linear sigma model (NLSM) of Goldstone bosons [42], a Lagrangian origin along with the structure constants of a kinematic algebra has been identified in [44]. This new formulation of the NLSM can be derived from higher dimensional YM theory [45], and a string-inspired higher-derivative extension. We hope that our D-dimensional double-copy representations for tree-level amplitudes of (α R2 + α 2R3)-deformed gravity shed further light into these looplevel topics: either by unitarity or by using the BCJ-gauge currents as building blocks for loop amplitudes that universally represent tree-level subdiagrams.
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