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Crossing Symmetric Dispersion Relations without Spurious Singularities

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arxiv 2305.03669 v2 pith:SKGSH5X6 submitted 2023-05-05 hep-th

classification hep-th
keywords dispersionfieldcrossing-symmetricrelationsingularitiesspuriousbootstrapconformal
verification ladder T0 review T1 audit T2 compute T3 formal
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Recently, there has been renewed interest in a crossing-symmetric dispersion relation from the 1970s due to its implications for both regular quantum field theory and conformal field theory. However, this dispersion relation introduces nonlocal spurious singularities and requires additional locality constraints for their removal, a process that presents considerable technical challenges. In this Letter, we address this issue by deriving a new crossing-symmetric dispersion relation that is free of spurious singularities, resulting in a compact form of the contact terms in crossing-symmetric blocks. Our results establish a solid foundation for the Polyakov bootstrap in conformal field theories and the crossing-symmetry S-matrix bootstrap in quantum field theories.

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Cited by 2 Pith papers

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  1. Bootstrapping black holes at low impact parameter

    hep-th 2026-07 conditional novelty 7.0 of 10

    After subtracting the eikonal carrier, the residual SDR spectrum in six dimensions organizes into a cap-saturated low-impact band, an empty gap, and Regge-like ridges whose weak-coupling edge is the G_N=0 baseline.

  2. The EFT Bootstrap at Finite $M_{PL}$

    hep-th 2025-01 conditional novelty 7.0 of 10

    One-loop gravity effects make forward-limit positivity bounds ill-defined for massless scalar-gravity EFTs, forcing non-forward dispersion relations that shift the tree-level bounds by order-one factors.

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