Non-Abelian gauged supergravities as double copies

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157

182

The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of black-hole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point examples. For concreteness, we focus on the double copy of QCD with massive quarks, for which we work out the gravitational Lagrangian up to quartic scalar and vector-scalar couplings. We find new gauge-invariant double-copy formulae for tree-level amplitudes with two distinct-flavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the well-known Kawai-Lewellen-Tye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

Section: Three-vertex For Spinmentioning

confidence: 99%

Double copy for massive quantum particles with spin

Johansson

Ochirov

2019

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157

182

“…Beyond tree level, many BCJ numerators are known for specific (multi-)loop amplitudes in various (super-)Yang-Mills theories [2,[5][6][7][8][29][30][31][32][33][34][35] and also for multi-loop form factors [36][37][38]. Other (more exotic) gauge theories [3,4,8,9,11,12,[39][40][41][42], as well as string theories [43][44][45][46][47], have been observed to obey color-kinematics duality, but in these cases the BCJ numerators are not known beyond the simplest amplitudes.…”

Section: Introductionmentioning

confidence: 99%

On the kinematic algebra for BCJ numerators beyond the MHV sector

Chen

Johansson

Teng

et al. 2019

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106

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 ).

“…Examples of this include applications of unitarity at one [7][8][9][10][11][12][13][14][15][16], two [17][18][19] and three loops [20] to the computation of bending angles, and classical and quantum corrections to the gravitational potential. An important tool in the amplitude arsenal is the colour-kinematics and double-copy duality [21][22][23], which makes explicit an intriguing interplay between colour and kinematics of amplitudes in Yang-Mills and other theories [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. This also allows one to construct gravity amplitudes from Yang-Mills ones once the latter are expressed in a so-called BCJ form, in a similar spirit to the KLT relations [39].…”

Section: Jhep07(2021)047mentioning

confidence: 99%

A new gauge-invariant double copy for heavy-mass effective theory

Brandhuber

Chen

Travaglini

et al. 2021

We propose a new form of the colour-kinematics/double-copy duality for heavy-mass effective field theories, which we apply to construct compact expressions for tree amplitudes with heavy matter particles in Yang-Mills and in gravity to leading order in the mass. In this set-up, the new BCJ numerators are fixed uniquely and directly written in terms of field strengths, making gauge invariance manifest. Furthermore, they are local and automatically satisfy the Jacobi relations and crossing symmetry. We construct these BCJ numerators explicitly up to six particles. We also discuss relations of the BCJ numerators in the heavy-mass effective theory with those in pure Yang-Mills amplitudes.