Simmons-Duffin, David and Stanford, Douglas and Witten, Edward (2018) A spacetime derivation of the Lorentzian OPE inversion formula. Journal of High Energy Physics, 2018 (7). Art. No. 85. ISSN 1126-6708. doi:10.1007/JHEP07(2018)085. https://resolver.caltech.edu/CaltechAUTHORS:20180713-090329998
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Abstract
Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.
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| Additional Information: | © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. First Online: 12 July 2018. Article funded by SCOAP3. We thank Simon Caron-Huot, Abhijit Gadde, Denis Karateev, Petr Kravchuk, Eric Perlmutter, and Shu-Heng Shao for discussions. DS is supported by Simons Foundation grant 385600. DSD is supported by Simons Foundation grant 488657. EW is supported in part by NSF Grant PHY-1606531. | ||||||||||
| Group: | Walter Burke Institute for Theoretical Physics | ||||||||||
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| Subject Keywords: | Conformal and W Symmetry, Conformal Field Theory | ||||||||||
| Issue or Number: | 7 | ||||||||||
| DOI: | 10.1007/JHEP07(2018)085 | ||||||||||
| Record Number: | CaltechAUTHORS:20180713-090329998 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180713-090329998 | ||||||||||
| Official Citation: | Simmons-Duffin, D., Stanford, D. & Witten, E. J. High Energ. Phys. (2018) 2018: 85. https://doi.org/10.1007/JHEP07(2018)085 | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 87817 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | George Porter | ||||||||||
| Deposited On: | 13 Jul 2018 17:20 | ||||||||||
| Last Modified: | 15 Nov 2021 20:52 |
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