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Abstract
We explore various tree-level double copy constructions for amplitudes including massive particles with spin. By working in general dimensions, we use that particles with spins s ≤ 2 are fundamental to argue that the corresponding double copy relations partially follow from compactification of their massless counterparts. This massless origin fixes the coupling of gluons, dilatons and axions to matter in a characteristic way (for instance fixing the gyromagnetic ratio), whereas the graviton couples universally reflecting the equivalence principle. For spin-1 matter we conjecture all-order Lagrangians reproducing the interactions with up to two massive lines and we test them in a classical setup, where the massive lines represent spinning compact objects such as black holes. We also test the amplitudes via CHY formulae for both bosonic and fermionic integrands. At five points, we show that by applying generalized gauge transformations one can obtain a smooth transition from quantum to classical BCJ double copy relations for radiation, thereby providing a QFT derivation for the latter. As an application, we show how the theory arising in the classical double copy of Goldberger and Ridgway can be naturally identified with a certain compactification of mathcal{N} = 4 Supergravity.
Highlights
We explore various tree-level double copy constructions for amplitudes including massive particles with spin
We show that by applying generalized gauge transformations one can obtain a smooth transition from quantum to classical BCJ double copy relations for radiation, thereby providing a QFT derivation for the latter
We show how the theory arising in the classical double copy of Goldberger and Ridgway can be naturally identified with a certain compactification of N = 4 Supergravity
Summary
The Bern-Carrasco-Johansson double copy program [1] has demonstrated how certain gravitational quantities can be obtained as a square of gauge-theory ones. By promoting QED to QCD, studying higher multiplicity amplitudes and the relevant cases for two massive lines, we will identify the gravitational theories obtained by this construction, as promised in [47]. A sum over I = 1, 2, the flavour index, is implicit and “quartic terms” denote contact interactions between two matter lines that we will identify These actions will be constructed in general dimensions from simple considerations such as 1) classical behaviour and 2) massless limit/compactification in the string frame. In general dimension we will see that the 0 ⊗ 1 theory is precisely the QFT version of the worldline model constructed by Goldberger and Ridgway in [22, 26] and later extended in [24, 27] to exhibit a classical double copy construction with spin This explains their findings on the fact that the classical double copy fixes g = 2 on the YM side, and precisely sets the dilaton/axion-matter coupling on the gravity side. Refs. [49, 80] have appeared, which have focused on scalars and have employed the compactification to construct the relevant gravitational amplitudes, AGn R,0
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