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Reconstructing S-matrix Phases with Machine Learning

Aurélien Dersy, Matthew D. Schwartz, Alexander Zhiboedov

18/8/23 Published in : arXiv:2308.09451

An important element of the S-matrix bootstrap program is the relationship between the modulus of an S-matrix element and its phase. Unitarity relates them by an integral equation. Even in the simplest case of elastic scattering, this integral equation cannot be solved analytically and numerical approaches are required. We apply modern machine learning techniques to studying the unitarity constraint. We find that for a given modulus, when a phase exists it can generally be reconstructed to good accuracy with machine learning. Moreover, the loss of the reconstruction algorithm provides a good proxy for whether a given modulus can be consistent with unitarity at all. In addition, we study the question of whether multiple phases can be consistent with a single modulus, finding novel phase-ambiguous solutions. In particular, we find a new phase-ambiguous solution which pushes the known limit on such solutions significantly beyond the previous bound.

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Phase I & II research project(s)

  • String Theory
  • Field Theory

Phase III direction(s)

  • Holography and bulk-boundary correspondence

KAM, Lyapunov exponents, and the Spectral Dichotomy for typical one-frequency Schrodinger operators

Regularity theory for nonlocal obstacle problems with critical and subcritical scaling

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The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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