A spacetime derivation of the Lorentzian OPE inversion formula
David Simmons-Duffin, Douglas Stanford, and Edward Witten
TL;DR
This paper presents a new spacetime-based derivation of the Lorentzian OPE inversion formula, providing insights into conformal field theories and the chaos regime in the SYK model.
Contribution
It offers a novel derivation method for the Lorentzian OPE inversion formula using Wick rotation, applicable in various dimensions, and clarifies aspects of the SYK model's chaos regime.
Findings
New spacetime derivation of the Lorentzian OPE inversion formula
Simplified derivation in two dimensions, more complex in higher dimensions
Insights into the chaos regime in the SYK model
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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