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- W3100328037 abstract "We derive a Lorentzian OPE inversion formula for the principal series of $sl(2,mathbb{R})$. Unlike the standard Lorentzian inversion formula in higher dimensions, the formula described here only applies to fully crossing-symmetric four-point functions and makes crossing symmetry manifest. In particular, inverting a single conformal block in the crossed channel returns the coefficient function of the crossing-symmetric sum of Witten exchange diagrams in AdS, including the direct-channel exchange. The inversion kernel exhibits poles at the double-trace scaling dimensions, whose contributions must cancel out in a generic solution to crossing. In this way the inversion formula leads to a derivation of the Polyakov bootstrap for $sl(2,mathbb{R})$. The residues of the inversion kernel at the double-trace dimensions give rise to analytic bootstrap functionals discussed in recent literature, thus providing an alternative explanation for their existence. We also use the formula to give a general proof that the coefficient function of the principal series is meromorphic in the entire complex plane with poles only at the expected locations." @default.
- W3100328037 created "2020-11-23" @default.
- W3100328037 creator A5008517051 @default.
- W3100328037 date "2019-06-01" @default.
- W3100328037 modified "2023-10-02" @default.
- W3100328037 title "A crossing-symmetric OPE inversion formula" @default.
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- W3100328037 doi "https://doi.org/10.1007/jhep06(2019)082" @default.
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