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arXiv · 2210.12147

Lorentzian inversion in non-relativistic and classical limits

Henry Maxfield·Zahra Zahraee
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Abstract

We study tools of the conformal bootstrap in simplifying limits, primarily a limit of large operator dimensions and small cross-ratios corresponding to non-relativistic physics in AdS. We show that T-channel conformal blocks give the classical limit of correlation functions to linear order in an interaction potential. We use the Lorentzian inversion formula to compute anomalous dimensions due to T-channel exchanges and compare with time-independent perturbation theory in AdS. These calculations include new results not restricted to any limit, including anomalous dimensions from stress-tensor exchange in general dimension. We also study a classical limit of large operator dimension and spin, in which the Lorentzian inversion formula is evaluated by saddle-point. Finally, we obtain a new `Lorentzian' inversion formula for non-relativistic AdS by taking a limit of the CFT inversion formula.

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Henry Maxfield, Zahra Zahraee. 2022-10-21. Lorentzian inversion in non-relativistic and classical limits. https://arxiv.org/abs/2210.12147

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