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arXiv · 1711.03816

A spacetime derivation of the Lorentzian OPE inversion formula

David Simmons-Duffin·Douglas Stanford·Edward Witten
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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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David Simmons-Duffin, Douglas Stanford, Edward Witten. 2017-11-10. A spacetime derivation of the Lorentzian OPE inversion formula. https://doi.org/10.1007/jhep07(2018)085

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