Twist Accumulation in Conformal Field Theory: A Rigorous Approach to the Lightcone Bootstrap
- Creators
- Pal, Sridip
- Qiao, Jiaxin
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Rychkov, Slava
Abstract
We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar quasiprimary operators (i.e. ϕ×ϕ) implies the existence of a family of quasiprimary operators Oτ,ℓ with spins ℓ→∞ and twists τ→2Δ_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 O_(h,h̅) with h→∞ and h̅→(c−1)/24 (the same is true with h and h¯ interchanged). We summarize the similarity of the two problems and propose a general formulation of the lightcone bootstrap.
Additional Information
© 2023 Springer Nature. Ideas of Quentin Lamouret [39] played a role at the genesis of this project. We thank Ying-Hsuan Lin, Dalimil Mazáč, Balt van Rees and Sylvain Ribault for useful discussions. When the project got initiated, SP was at the Institute for Advanced Study and he acknowledges a debt of gratitude for the funding provided by Tomislav and Vesna Kundic as well as the support from the grant DE-SC0009988 from the U.S. Department of Energy. SP also acknowledges the support by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics. JQ is grateful for the funding provided by École Normale Supérieure - PSL and the Simons Bootstrap Collaboration when this project was initiated in the workshop "Bootstrap 2022" at Porto University. JQ is supported by the Swiss National Science Foundation through the National Centre of Competence in Research SwissMAP and by the Simons Collaboration on Confinement and QCD Strings. SR is supported by the Simons Foundation grant 733758 (Simons Bootstrap Collaboration). Data availability statement: Data sharing is not applicable to this article as no datasets were generated or analyzed.Additional details
- Eprint ID
- 122155
- Resolver ID
- CaltechAUTHORS:20230705-476466000.24
- Tomislav and Vesna Kundic
- Department of Energy (DOE)
- DE-SC0009988
- Department of Energy (DOE)
- DE-SC0011632
- Walter Burke Institute for Theoretical Physics, Caltech
- École Normale Supérieure
- Simons Foundation
- 733758
- Swiss National Science Foundation (SNSF)
- Created
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2023-07-07Created from EPrint's datestamp field
- Updated
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2023-07-07Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics