Abstract
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at tree-level and one loop. The double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes which are naturally organized as polynomials in the gauge coupling constant.
Highlights
Bern, Carrasco and Johansson (BCJ) proposed a set of Lie-algebraic relations for the kinematic building blocks of gauge-theory loop-level amplitudes [3, 4], which mirror analogous relations obeyed by the corresponding color building blocks
The analysis described can be carried out in five dimensions with similar conclusions: a five-dimensional Yang-Mills/Einstein supergravity theories (YMESGTs) in the generic Jordan family can be described as a double-copy of the half-maximal sYM theory and a vector-scalar theory with trilinear couplings
It is no surprise that MaxwellEinstein supergravity theories (MESGTs) obtained directly from N = 8 supergravity have a doublecopy structure inherited from that of the parent theory
Summary
It has long been known [1, 2] that, at tree level, the scattering amplitudes of gravity and supergravity theories related to string theory compactifications on tori exhibit a double-copy structure, being expressible as sums of products of amplitudes of certain gauge theories. The integrands of gauge-theory amplitudes are best arranged in a cubic (trivalent) graphbased presentation that exhibits a particular duality between their color and kinematic numerator factors Once such a presentation is obtained, the double-copy relation between the integrands of gauge-theory and gravity amplitudes extents smoothly to loop level. The Grassmann parameters that may appear in ni and/or ni are inherited by the corresponding supergravity amplitudes; they imply a particular organization of the asymptotic states labeling supergravity amplitudes in multiplets of linearized supersymmetry Since these linearized transformations — given by shifts of the Grassmann parameters — are inherited from the supersymmetry transformations of the gauge-theory factors, they need not be the same as the natural linearized supersymmetry transformations following from the supergravity Lagrangian and a nontrivial transformation may be necessary to align the double-copy and Lagrangian asymptotic states.
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