Multitwist Trajectories and Decoupling Zeros in Conformal Field Theory
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1.
University of Waterloo
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2.
California Institute of Technology
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3.
Perimeter Institute
Abstract
Conformal Regge theory predicts the existence of analytically continued conformal field theory data for complex spin. How could this work when there are so many more operators with large spin compared to small spin? Using planar N=4 SYM as a test ground, we find a simple physical picture. Operators do organize themselves into analytic families but the continuation of the higher families have zeros in their structure operator product expansion constants for lower integer spins. They thus decouple. Newton's interpolation series technique is perfectly suited to this physical problem and will allow us to explore the complex spin half-plane.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Acknowledgement
We thank F. Aprile, B. Basso, C. Bercini, C-H. Chang, F. Coronado, S. Caron-Huot, N. Gromov, P. Kravchuk, V. Voloshyna, and X. Yin for enlightening discussions. We are especially grateful to Simon Caron-Huot for a most inspiring discussion in 2018, at the annual Simons Bootstrap Collaboration meeting at the Perimeter Institute. Some of the results obtained in this Letter were somehow anticipated by Simon already at that time (albeit using different tools/ideas). We thank several participants of the 2022 Simons bootstrap collaboration meeting for reminding us of the important Ref. [8]. Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. This work was additionally supported by a grant from the Simons Foundation (P. V.: No. 488661) and FAPESP Grants No. 2016/01343-7 and No. 2017/03303-1. D. S. D. is supported by Simons Foundation Grant No. 488657 (Simons Collaboration on the Nonperturbative Bootstrap) and a DOE Early Career Award under Grant No. DE-SC0019085.
Funding
Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. This work was additionally supported by a grant from the Simons Foundation (P. V.: No. 488661) and FAPESP Grants No. 2016/01343-7 and No. 2017/03303-1. D. S. D. is supported by Simons Foundation Grant No. 488657 (Simons Collaboration on the Nonperturbative Bootstrap) and a DOE Early Career Award under Grant No. DE-SC0019085.
Supplemental Material
The supplemental material includes complementary formulas, checks and discussions supporting the self-contained material in the main text.
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Additional details
- Government of Canada
- Natural Sciences and Engineering Research Council
- Province of Ontario
- Simons Foundation
- 488661
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- 2016/01343-7
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- 2017/03303-1
- Simons Foundation
- 488657
- United States Department of Energy
- DE-SC0019085
- SCOAP3
- Available
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2024-12-05Accepted
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Publication Status
- Published