A spacetime derivation of the Lorentzian OPE inversion formula

By David Simmons-Duffin, D. Stanford, E. Witten. Journal of High Energy Physics, 2017

233 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8a9ff307a886a0ab3abde6e6799c4ef3da379047

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Citations in the corpus

All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry (2018, background): “(3)We find that the result in [25] holds also in the case of non-identical external operators provided that the sum runs over half-integer h when p12 is odd.”
Light-ray operators in conformal field theory (2018, methodology): “endent of which point we choose for x ∞. The spurious dependence of formulas on x∞ will go away soon. 38Note that we do not place O(x,z) at inﬁnity before performing the Wick rotation, in contrast to [31]. The reason is that in our case the region of integration for 1,2 is independent of the positio”