A spacetime derivation of the Lorentzian OPE inversion formula

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

doi:10.1007/JHEP07(2018)085

A spacetime derivation of the Lorentzian OPE inversion formula

Journal Article · Thu Jul 12 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP07(2018)085· OSTI ID:1598252

Simmons-Duffin, David ^[1]; Stanford, Douglas ^[2]; Witten, Edward ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States); Institute for Advanced Study
Inst. for Advanced Study, Princeton, NJ (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Inst. for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1598252

Alternate ID(s):: OSTI ID: 22743403

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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A spacetime derivation of the Lorentzian OPE inversion formula

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