The $T^{μν}$ of the conformal scalars
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| Format: | Preprint |
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2026
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| _version_ | 1866915832718688256 |
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| author | Fraser-Taliente, Kit Fraser-Taliente, Ludo |
| author_facet | Fraser-Taliente, Kit Fraser-Taliente, Ludo |
| contents | We construct the unique primary energy-momentum tensor $T^{μν}$ for the conformal free scalar with scaling dimension $Δ=d/2-ζ$ as a sum of Gegenbauer polynomials. For integer $ζ$, the sum truncates at order $ζ$, compactly reproducing all known results; for the nonlocal case of real $ζ$, it is an infinite sum, with a two-parameter extension that reflects the nonuniqueness of the nonlocal geometric coupling. We find $T^{μν}$ by imposing off-shell conservation and tracelessness, and then directly solving the primary condition in momentum space. In the integer $ζ$ case, we reproduce the known two-point function, and confirm the match with the $T^{μν}$ computed from Juhl's formulae for the GJMS operators (the Weyl-covariant upgrades of $(-\partial^2)^ζ$), an equality following from the descent of Weyl covariance to conformal invariance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05311 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $T^{μν}$ of the conformal scalars Fraser-Taliente, Kit Fraser-Taliente, Ludo High Energy Physics - Theory We construct the unique primary energy-momentum tensor $T^{μν}$ for the conformal free scalar with scaling dimension $Δ=d/2-ζ$ as a sum of Gegenbauer polynomials. For integer $ζ$, the sum truncates at order $ζ$, compactly reproducing all known results; for the nonlocal case of real $ζ$, it is an infinite sum, with a two-parameter extension that reflects the nonuniqueness of the nonlocal geometric coupling. We find $T^{μν}$ by imposing off-shell conservation and tracelessness, and then directly solving the primary condition in momentum space. In the integer $ζ$ case, we reproduce the known two-point function, and confirm the match with the $T^{μν}$ computed from Juhl's formulae for the GJMS operators (the Weyl-covariant upgrades of $(-\partial^2)^ζ$), an equality following from the descent of Weyl covariance to conformal invariance. |
| title | The $T^{μν}$ of the conformal scalars |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.05311 |