Why is the Weyl double copy local in position space?
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Why is the Weyl double copy local in position space? / Luna, Andres; Moynihan, Nathan; White, Chris D. D.
In: Journal of High Energy Physics, Vol. 2022, No. 12, 046, 09.12.2022.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Why is the Weyl double copy local in position space?
AU - Luna, Andres
AU - Moynihan, Nathan
AU - White, Chris D. D.
PY - 2022/12/9
Y1 - 2022/12/9
N2 - The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space - and when this form will break - has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.
AB - The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space - and when this form will break - has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.
KW - Black Holes
KW - Classical Theories of Gravity
KW - Scattering Amplitudes
U2 - 10.1007/JHEP12(2022)046
DO - 10.1007/JHEP12(2022)046
M3 - Journal article
VL - 2022
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
SN - 1126-6708
IS - 12
M1 - 046
ER -
ID: 332121289