Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes

Abstract

We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators α F 3 and α 2 F 4 . 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 R 2 and α 2 R 3 operators. arXiv:1809.08103v1 [hep-th] 21 Sep 2018 45 A.3 Gauge algebra 47 B The explicit form of gauge scalars towards BCJ gauge 50 B.1 The local building block h 12345 50 B.2 An alternative expression for H 1234 51 B.3 The Berends-Giele version H 12345 52 C Deriving a BCJ representation for (YM+F 3 +F 4 ) amplitudes 52 -1 -1 The low-energy effective action of the open bosonic string involves another operator ∼ ζ2α 2 F 4 at the mass dimensions in (1.1) which will not be discussed in this article. Said ζ2α 2 F 4 -operator is also known from the superstring and cannot be reconciled with the BCJ duality [18]. 2 See [ 23,24] for earlier work on the interplay of the KLT relations at the three-and four-point level with gravitational matrix elements of R 2 , R 3 operators and F 3 , F 4 -deformed gauge-theory amplitudes.3 In slight abuse of terminology, we will usually refer to the matrix elements from higher-mass-dimension operators as "amplitudes". In the case at hand, we will be interested in contributions from single-or doubleinsertions of α R 2 operators and single-insertions of α 2 R 3 4 See [27,28] for generating series of Berends-Giele currents, their non-linear gauge transformations and BCJ gauge in ten-dimensional SYM.5 Said higher-derivative extension of the NLSM is defined by the ζ2α 2 -order of abelian Z-theory [44].

On the kinematic algebra for BCJ numerators beyond the MHV sector

“…The vector and tensor currents can then be formally viewed as certain off-shell fields that are being recursively constructed. Previous work have systematically analyzed the construction of BCJ numerators through Berends-Giele recursion [21,23,94], however in that work a non-linear gauge transformation was needed to make the off-shell numerators obey color-kinematics duality. Such gauge transformations were constructed through an iterative process that generated new formulas at each step.…”

One-loop correlators and BCJ numerators from forward limits

“…p or multiparticle labels. This subsection simply collects the definitions relevant to later equations, and the reader is referred to [61,106,109] for further background.…”

Algorithmic construction of SYM multiparticle superfields in the BCJ gauge

“…This may give rise to a systematic derivation of the H ′ A,B,C redefinitions via OPE calculations and it is an interesting question left to the future. BCJ numerators were constructed for gauge theories deformed by α ′ F 3 and α ′ 2 F 4 interactions by finding appropriate α ′ corrections to the H P fields [24]. Since low-multiplicity examples show that these corrections can also be written in terms of α ′ -corrected H A,B,C in a similar manner as discussed in this paper, one may wonder whether the all-multiplicity formulas found here can be applied with minimal changes to the setup of [24].…”