Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

TL;DR

This work demonstrates that a broad class of ${N=2}$ Maxwell–Einstein and Yang–Mills/Einstein supergravity theories in four and five dimensions can be constructed via a double-copy from two gauge theories: a pure ${N=2}$ super Yang–Mills factor and a dimensionally reduced bosonic Yang–Mills factor augmented by cubic scalar couplings. The authors identify a symplectic frame in which double-copy amplitudes map cleanly onto the supergravity Lagrangian, and show that gauged YMESGTs (generic Jordan family) arise from compact gaugings implemented through these cubic couplings, with non-abelian vector interactions encoded in the gauge-theory side. The paper provides explicit tree-level and one-loop results, including compact expressions for superamplitudes organized as polynomials in the gauge coupling, and confirms color/kinematics duality for the YM–scalar sector up to at least five points. These results establish a concrete, computable framework for perturbative amplitudes in a wide class of ${N=2}$ gauged supergravities, with potential extensions to hypermultiplets and broader gaugings. The work paves the way for systematic multi-loop studies and possible AdS/CFT connections of double-copy structures in diverse supergravity theories.

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.

Figures (2)

• Figure 1: The three types of diagrams that contribute at different orders in the $g'$ coupling to the box numerator of a four-scalar one-loop amplitude. All distinct cyclic permutations of these diagrams should be included. Dashed lines denote scalar fields while curly lines denote vector fields. Note that quartic-scalar interactions are implicitly included in these diagrams, according to their power in the $g'$ coupling.
• Figure 2: The three types of diagrams that contribute to the box numerator in YMESG can be obtained through a double copy between the diagrams in fig. \ref{['OneLoopYMFigure']} and a sYM numerator that obeys color/kinematics duality. All distinct cyclic permutations of these diagrams should be included. We use dashed lines to denote scalar fields, curly lines to denote vector fields or vector multiplets (as the case may be) and wavy lines to denote the graviton multiplet.