A spacetime derivation of the Lorentzian OPE inversion formula

David Simmons-Duffin; Douglas Stanford; Edward Witten

doi:10.1007/JHEP07(2018)085

A spacetime derivation of the Lorentzian OPE inversion formula

David Simmons-Duffin, Douglas Stanford, Edward Witten

Research output: Contribution to journal › Article › peer-review

165 Scopus citations

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.

Original language	English (US)
Article number	85
Journal	Journal of High Energy Physics
Volume	2018
Issue number	7
DOIs	https://doi.org/10.1007/JHEP07(2018)085
State	Published - Jul 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

Keywords

Conformal Field Theory
Conformal and W Symmetry

Access to Document

10.1007/JHEP07(2018)085

Cite this

@article{8517ed642fe0466eb166a47a10d510ec,

title = "A spacetime derivation of the Lorentzian OPE inversion formula",

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.",

keywords = "Conformal Field Theory, Conformal and W Symmetry",

author = "David Simmons-Duffin and Douglas Stanford and Edward Witten",

note = "Publisher Copyright: {\textcopyright} 2018, The Author(s).",

year = "2018",

month = jul,

day = "1",

doi = "10.1007/JHEP07(2018)085",

language = "English (US)",

volume = "2018",

journal = "Journal of High Energy Physics",

issn = "1126-6708",

publisher = "Springer Verlag",

number = "7",

}

TY - JOUR

T1 - A spacetime derivation of the Lorentzian OPE inversion formula

AU - Simmons-Duffin, David

AU - Stanford, Douglas

AU - Witten, Edward

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - Conformal Field Theory

KW - Conformal and W Symmetry

UR - http://www.scopus.com/inward/record.url?scp=85049964906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049964906&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2018)085

DO - 10.1007/JHEP07(2018)085

M3 - Article

AN - SCOPUS:85049964906

SN - 1126-6708

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 7

M1 - 85

ER -

A spacetime derivation of the Lorentzian OPE inversion formula

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this