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Article Dans Une Revue Communications in Mathematical Physics Année : 2023

Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap

Résumé

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. $\phi\times \phi$) implies the existence of a family of primary operators $\mathcal{O}_{\tau, \ell}$ with spins $\ell \rightarrow \infty$ and twists $\tau \rightarrow 2 \Delta_{\phi}$ 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.

Dates et versions

hal-03919955 , version 1 (03-01-2023)

Identifiants

Citer

Sridip Pal, Jiaxin Qiao, Slava Rychkov. Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap. Communications in Mathematical Physics, 2023, 402 (3), pp.2169-2214. ⟨10.1007/s00220-023-04767-w⟩. ⟨hal-03919955⟩
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