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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.04893 |
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| _version_ | 1866908663640227840 |
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| author | Pal, Sridip Qiao, Jiaxin Rychkov, Slava |
| author_facet | Pal, Sridip Qiao, Jiaxin Rychkov, Slava |
| contents | We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar primary operators (i.e. $ϕ\times ϕ$) implies the existence of a family of primary operators $\mathcal{O}_{τ, \ell}$ with spins $\ell \rightarrow \infty$ and twists $τ\rightarrow 2 Δ_ϕ$ in the same OPE spectrum. A similar twist-accumulation result is proven for any two-dimensional Virasoro-invariant, modular-invariant, unitary CFT with a normalizable vacuum and central charge $c > 1$, where we show that a twist gap in the spectrum of Virasoro primaries implies the existence of a family of Virasoro primaries $\mathcal{O}_{h, \bar{h}}$ with $h \rightarrow \infty$ and $\bar{h} \rightarrow \frac{c - 1}{24}$ (the same is true with $h$ and $\bar{h}$ interchanged). We summarize the similarity of the two problems and propose a general formulation of the lightcone bootstrap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_04893 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap Pal, Sridip Qiao, Jiaxin Rychkov, Slava High Energy Physics - Theory We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar primary operators (i.e. $ϕ\times ϕ$) implies the existence of a family of primary operators $\mathcal{O}_{τ, \ell}$ with spins $\ell \rightarrow \infty$ and twists $τ\rightarrow 2 Δ_ϕ$ in the same OPE spectrum. A similar twist-accumulation result is proven for any two-dimensional Virasoro-invariant, modular-invariant, unitary CFT with a normalizable vacuum and central charge $c > 1$, where we show that a twist gap in the spectrum of Virasoro primaries implies the existence of a family of Virasoro primaries $\mathcal{O}_{h, \bar{h}}$ with $h \rightarrow \infty$ and $\bar{h} \rightarrow \frac{c - 1}{24}$ (the same is true with $h$ and $\bar{h}$ interchanged). We summarize the similarity of the two problems and propose a general formulation of the lightcone bootstrap. |
| title | Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2212.04893 |