Extension of positivity bounds to non-local theories: IR obstructions to Lorentz invariant UV completions

Understand

We derive positivity bounds on low energy effective field theories which admit gapped, analytic, unitary, Lorentz invariant, and possibly non-local UV completions, by considering 2 to 2 scatterings of Jaffe fields whose Lehmann-K\"{a}ll\'{e}n spectral density can grow exponentially.

• Several properties of S-matrix, such as analyticity properties, are assumed in our derivation.
• Interestingly, we find that some of the positivity bounds obtained in the literature, such as sub-leading order forward-limit bounds, must be satisfied even when UV completions fall into non-localizable theories in Jaffe's language, unless momentum space Wightman functions grow too rapidly at high energy.
• Under this restriction on the growth rate, such bounds may provide IR obstructions to analytic, unitary, and Lorentz invariant UV completions.