BCJ numerators from reduced Pfaffian

Du, Yi-Jian; Teng, Fei

doi:10.1007/jhep04(2017)033

Cited by 84 publications

(110 citation statements)

References 36 publications

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“…Another example of eq. (6.22) at n = 6 is 25) which can also be directly verified. We have checked the validity of eq.…”

Section: Generalized Binary Bcj Relations and Disconnected Topologiessupporting

confidence: 61%

“…It is curious to note that the objects that the kinematic Lie algebra should compute, the kinematic BCJ numerators, are under better control than the algebra itself. Numerators that manifest the color-kinematics duality have been constructed at any multiplicity for tree-level amplitudes in pure Yang-Mills theory [20][21][22][23][24][25][26][27]. For supersymmetric Yang-Mills theory, it has been observed that a recursive construction similar to Berends-Giele recursion [28] can be used to generate BCJ numerators after using appropriate non-linear gauge transformations [23].…”

Section: Introductionmentioning

confidence: 99%

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On the kinematic algebra for BCJ numerators beyond the MHV sector

Chen

Johansson

Teng

et al. 2019

J. High Energ. Phys.

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106

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The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain O (ε i ·ε j ) 2 terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents controls the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.1 Cubic interactions are obtained by the replacement Tr([A µ , A ν ] 2 ) → − 1 2 (B µν ) 2 +Tr([A µ , A ν ]B µν ).

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“…Another example of eq. (6.22) at n = 6 is 25) which can also be directly verified. We have checked the validity of eq.…”

Section: Generalized Binary Bcj Relations and Disconnected Topologiessupporting

confidence: 61%

Section: Introductionmentioning

confidence: 99%

On the kinematic algebra for BCJ numerators beyond the MHV sector

Chen

Johansson

Teng

et al. 2019

J. High Energ. Phys.

Self Cite

106

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“…Effective non-gravitational theories for which a double-copy construction is known include the Dirac-Born-Infeld and the special Galileon theories, as well as the nonlinear sigma model [38,39,40,41,42,43,44]. Double-copy structures have also been identified for various string-theory amplitudes, [45,46,47,48,49,50,51,52,53], within the Cachazo-He-Yuan formalism [54,55,56,57,58], in the context of ambitwistor string theories [59], and at the level of linearized supermultiplets [60,61,62,63,64].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…While various Yang-Mills-Einstein theories have been investigated in detail [65,40,66,67,68,69,70,57,71], amplitudes in gauged supergravities have been comparatively less studied. Very recently, the current authors formulated a double-copy construction for simple U(1) R gauged N = 2 supergravities that admit Minkowski vacua [70].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Non-Abelian gauged supergravities as double copies

Chiodaroli

Günaydın

Johansson

et al. 2019

J. High Energ. Phys.

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Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged R-symmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for double-copy constructions of Abelian and non-Abelian gaugings of N = 8 supergravity with these properties. They are generally obtained as the double copy of a spontaneously-broken (possibly supersymmeric) gauge theory and a theory with explicitly-broken supersymmetry. We first identify purely-adjoint deformations of N = 4 super-Yang-Mills theory that preserve the duality between color and kinematics. A combination of Higgsing and orbifolding yields the needed duality-satisfying gauge-theory factors with multiple matter representations. We present three explicit examples. Two are Cremmer-Scherk-Schwarz gaugings with unbroken N = 6, 4 supersymmetry and U (1) gauge group. The third has unbroken N = 4 supersymmetry and SU (2)× U (1) gauge group. We also discuss examples in which the double-copy method gives theories with explicitly-broken supersymmetry.

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“…With the guidance of the conjectured pattern in [19], rigorous proof of the conjecture has been given in [31] by carefully dealing with the CHY-integrands of sEYM theory, especially the Pfaffian structure. Based on these results, expansions for multi-trace EYM amplitudes as well as nonlinear sigma model (NLSM) amplitudes have been given in [32,33], again using the gauge symmetry considerations plus the manipulations of the CHY-integrands. The second important result coming from the CHY formalism is that different theories have some deep connections, where KLT-like relations are just a reflection of them.…”

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confidence: 99%

Expansion of Einstein-Yang-Mills theory by differential operators

Feng

Zhou

2019

Phys. Rev. D

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The factorization form of the integrands in the Cachazo-He-Yuan (CHY) formalism makes the generalized Kawai-Lewellen-Tye (KLT) relations manifest, thus amplitudes of one theory can be expanded in terms of the amplitudes of another theory. Although this claim seems a rather natural consequence of the above structure, finding the exact expansion coefficients to express an amplitude in terms of another amplitudes is, nonetheless, a nontrivial task despite many efforts devoted to it in the literature. In this paper, we propose a new strategy based in using the differential operators introduced by Cheung, Shen and Wen, and taking advantage of the fact these operators already relate the amplitudes of different theories. Using this new method, expansion coefficients can be found effectively.Although the method should be general, to demonstrate the idea, we focus on the expansion of single trace Einstein-Yang-Mills (sEYM) amplitudes in the Kleiss-Kuijf (KK)-basis and Bern-Carrasco-Johansson (BCJ)-basis of Yang-Mills theory. Using the new method, the general recursive expansion to the KK-basis has been reproduced. The expansion to the BCJ-basis is a more difficult problem. Using the new method, we have worked out the details for sEYM with one, two and three gravitons. As a by-product, profound relations among two kinds of expansion coefficients, i.e., the expansion of sEYM amplitudes to the BCJ basis of YM theory and the expansion of any color ordered Yang-Mills amplitudes to its BCJ-basis, have been observed. . The corresponding author is Kang Zhou. 6.2.1 Another derivation 42 6.3 The case with three gravitons 44 7. Conclusion and discussion 49 A. Terms with index circle structure 51 B. General discussions of manifestly gauge invariant functions 53 B.1 Having only one polarization vector 54 B.2 Having two polarization vectors 55 B.3 Having three polarization vectors 56 -1 -C. Some calculation details using differential operators 59 1 See section 5 of [18] for a comprehensive up-to-date list of the theories connected by double-copy relations.-2 -copy form (1.3). However, such a triviality is just an illusion. When trying to get the exact expansion coefficients C, one will find it is very difficult task. If we use the expression (1.4) directly, one needs to do the sum over (n − 3)! terms. Since analytical expressions for both parts A L (n − 1, n, σ, 1) and S[σ| σ] are very complicated, it is no wonder why in the practice no one uses this method except for some special cases 2 . Many efforts have been devoted to avoid the mentioned technical difficulties. In [21], using the string theory, the single trace Einstein-Yang-Mills (sEYM) amplitudes with just one graviton have been expanded in terms of the color ordered Yang-Mills (YM) amplitudes. In [22], using the heterotic string theory, evidence of the expansion of general EYM amplitudes in terms of YM amplitudes has also been presented, but explicit expansions are done only for some special cases, such as up to three gravitons, or up to two color traces. In [23], using the fa...

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BCJ numerators from reduced Pfaffian

Cited by 84 publications

References 36 publications

On the kinematic algebra for BCJ numerators beyond the MHV sector

On the kinematic algebra for BCJ numerators beyond the MHV sector

Non-Abelian gauged supergravities as double copies

Expansion of Einstein-Yang-Mills theory by differential operators

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