Matrix moment approach to positivity bounds and UV reconstruction from IR

TL;DR

This paper extends the matrix moment approach to derive positivity bounds for multi-field EFTs and demonstrates how to reconstruct UV spectra from IR data, matching numerical bounds and enabling UV insights.

Contribution

It generalizes the moment problem formalism to matrix cases for multiple fields and shows how to reverse engineer UV spectra from EFT coefficients.

Findings

Derived optimal positivity bounds for multi-field theories.

Matched bounds with existing numerical methods.

Successfully reconstructed UV spectra from IR data in examples.

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.