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Matrix moment approach to positivity bounds and UV reconstruction from IR

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arxiv 2411.11964 v1 pith:M4AQTW5H submitted 2024-11-18 hep-th gr-qchep-ph

Shi-Lin Wan , Shuang-Yong Zhou This is my paper · ORCID
classification hep-thgr-qchep-ph
keywords boundsmomentapproachfieldmatrixpositivitytheoriesproblem
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abstract

Positivity bounds in effective field theories (EFTs) can be extracted through the moment problem approach, utilizing well-established results from the mathematical literature. We generalize this formalism using the matrix moment approach to derive positivity bounds for theories with multiple field components. The sufficient conditions for obtaining optimal bounds are identified and applied to several example field theories, yielding results that match precisely the numerical bounds computed using other methods. The upper unitarity bounds can also be easily harnessed in the matrix case. Furthermore, the moment problem formulation also provides a means to reverse engineer the UV spectrum from the EFT coefficients, often uniquely, as explicitly demonstrated in examples such as string amplitudes and the $stu$ kink theory.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Unitary Dual-Resonance S-matrices

    hep-th 2026-07 conditional novelty 7.0 of 10

    Smearing Veneziano blocks over continuous Regge slopes yields local, analytic, crossing-symmetric S-matrices with full partial-wave unitarity and controllable second-sheet resonances.

  2. Splitting Regions and Shrinking Islands from Higher Point Constraints

    hep-th 2025-06 conditional novelty 7.0 of 10

    Imposing 5-point split conditions and unitarity bounds selects the string beta function as the unique 4-point amplitude, up to equal-mass infinite spin towers.

  3. Scalar weak gravity bound from full unitarity

    hep-th 2025-02 conditional novelty 7.0 of 10

    For a shift-symmetric scalar EFT with gravity, unitarity and dispersion relations imply Λ/M_P < 2.38 \tilde{g}_2^{1/5} and, in an improved smeared version, Λ^2/M_P^2 < 0.0115 |\tilde{g}_2|.

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