Positivity in Multifield Effective Field Theories.

Area of Science:

• Theoretical Physics
• High Energy Physics
• Cosmology

Background:

• Positivity bounds constrain effective field theories (EFTs) based on causality and unitarity.
• Traditional methods for deriving these bounds are often incomplete for multifield EFTs with multiple low-energy modes.

Purpose of the Study:

• To present a general and complete method for obtaining positivity bounds in multifield EFTs.
• To establish a connection between positivity bounds and geometric problems solvable with semidefinite programming (SDP).

Main Methods:

• The study extends beyond simple elastic scattering to analyze more complex scattering amplitudes.
• The allowed parameter space is identified as the dual to a spectrahedron, derived from amplitude crossing symmetries.
• Finding optimal bounds is framed as a geometric problem of identifying extremal rays of a spectrahedron, solved analytically for simple cases and numerically via SDP for complex ones.

Main Results:

• The developed SDP approach provides complete positivity bounds for generic multifield EFTs.
• This method was successfully applied to various well-motivated examples in particle physics and cosmology, including theories with scalars, vectors, fermions, and gravitons.
• The SDP approach yields results that are either improvements on existing bounds or entirely novel.

Conclusions:

• The SDP formulation offers a powerful and efficient numerical tool for deriving positivity bounds in EFTs.
• This generalized method overcomes limitations of previous techniques, providing more comprehensive constraints for multifield theories.
• The findings have significant implications for model building and exploring the landscape of fundamental physics.