Multipole expansion at the level of the action in d-dimensions

Amalberti, Loris; Larrouturou, Francois; Yang, Zixin

Preprint

PUBDB-2023-07357

Multipole expansion at the level of the action in d-dimensions

Amalberti, L. (Corresponding author)Extern*DESY* ; Larrouturou, F.DESY* ; Yang, Z.DESY*

2023

[10.3204/PUBDB-2023-07357]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2023-07357

Report No.: DESY-23-200; arXiv:2312.02868

Abstract: In this paper we study the multipole expansion of the long-wavelength effective action for ra-diative sources in (d+1) spacetime dimensions. We present detailed expressions for the multipolemoments for the case of scalar-, electromagnetic-, and (linearized) gravitational-wave emission. Forelectromagnetism and gravity, we derive expressions for the odd-parity, magnetic-type momentsas SO(d) duals of the ones traditionally used in the literature. The d-dimensional case features anovel set of ‘Weyl-type’ moments, coupling to the spatial part of the Weyl tensor, which are absentin three dimensions. Agreement is found in the overlap with previous known results, notably inthe d → 3 limit. Due to its reliance on dimensional regularization, the results presented here playa crucial role for the further development of the Effective Field Theory approach to gravitationaldynamics, and in particular for the computation of the gravitational-wave flux, starting at thethird post-Newtonian order.

Keyword(s): expansion, multipole ; tensor, Weyl ; space-time, dimension ; dimension, 3 ; regularization, dimensional ; gravitational radiation, flux ; gravitational radiation, emission ; gravitation ; effective field theory ; duality ; overlap ; effective action