A spacetime derivation of the Lorentzian OPE inversion formula

Creators: Simmons-Duffin, David; Stanford, Douglas; Witten, Edward

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.

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.

Attached Files

Published - Simmons-Duffin2018_Article_ASpacetimeDerivationOfTheLoren.pdf

Submitted - 1711.03816

Files

Simmons-Duffin2018_Article_ASpacetimeDerivationOfTheLoren.pdf

Files (1.6 MB)

Name	Size	Download all
1711.03816 md5:278fbba45d7355e89c4ca380b9f9577f	767.1 kB	Download
Simmons-Duffin2018_Article_ASpacetimeDerivationOfTheLoren.pdf md5:a1edf1fc5e6d27848c1eabb02c7c3ff3	799.2 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes