Celestial Conformal Primaries in Effective Field Theories
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914679101587456 |
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| author | Mitra, Prahar |
| author_facet | Mitra, Prahar |
| contents | Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative holographic CFT$_d$ by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously that conformal primary operators with $Δ\in \frac{d}{2} + i {\mathbb R}$ form a basis for massless one-particle representations. In this paper, we consider more general conformal primary operators with $Δ\in {\mathbb C}$ and show that completeness, normalizability, and consistency with CPT implies that we must restrict the scaling dimensions to either $Δ\in \frac{d}{2} + i {\mathbb R}$ or $Δ\in {\mathbb R}$. Unlike those with $Δ\in \frac{d}{2} + i {\mathbb R}$, the conformal primaries with $Δ\in {\mathbb R}$ can be constructed without knowledge of the UV and can therefore be defined in effective field theories. With additional analyticity assumptions, we can restrict $Δ\in 2 - {\mathbb Z}_{\geq0}$ or $Δ\in \frac{1}{2}-{\mathbb Z}_{\geq0}$ for bosonic or fermionic operators, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Celestial Conformal Primaries in Effective Field Theories Mitra, Prahar High Energy Physics - Theory Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative holographic CFT$_d$ by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously that conformal primary operators with $Δ\in \frac{d}{2} + i {\mathbb R}$ form a basis for massless one-particle representations. In this paper, we consider more general conformal primary operators with $Δ\in {\mathbb C}$ and show that completeness, normalizability, and consistency with CPT implies that we must restrict the scaling dimensions to either $Δ\in \frac{d}{2} + i {\mathbb R}$ or $Δ\in {\mathbb R}$. Unlike those with $Δ\in \frac{d}{2} + i {\mathbb R}$, the conformal primaries with $Δ\in {\mathbb R}$ can be constructed without knowledge of the UV and can therefore be defined in effective field theories. With additional analyticity assumptions, we can restrict $Δ\in 2 - {\mathbb Z}_{\geq0}$ or $Δ\in \frac{1}{2}-{\mathbb Z}_{\geq0}$ for bosonic or fermionic operators, respectively. |
| title | Celestial Conformal Primaries in Effective Field Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.09256 |