Positivity vs. Lorentz-violation: an explicit example
Katsuki Aoki, Shinji Mukohyama, and Ryo Namba
TL;DR
This paper explores how Lorentz-violating multi-field scalar theories influence effective single-field theories, demonstrating potential violations of positivity bounds under certain mass hierarchy conditions.
Contribution
It provides a concrete example of order-unity violation of positivity bounds in Lorentz-breaking scalar theories with hierarchical masses.
Findings
Positivity bounds can be violated in Lorentz-violating theories.
Hierarchy of masses affects the validity of positivity bounds.
Explicit example demonstrating these effects is provided.
Abstract
We show how a class of multi-field scalar-field theories in a Lorentz-breaking background imposes consistency conditions on its effective theory of a single field and provides an example of order-unity violation of a naively applied positivity bound, assuming a large hierarchy between the masses of the lightest field and the others.
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