Determine the relation between linear instabilities and strong coupling

Determine whether the classical linear instabilities of the Lorentz-violating Kalb–Ramond field about a nonzero Lorentz-breaking background are related to strong-coupling behavior by analyzing the perturbative action, kinetic matrix, canonical normalization, nonlinear interaction scale, and strong-coupling scale.

Background

The paper distinguishes the growing eigenmodes found on the fixed Schwarzschild background from strong-coupling and runaway effects reported for other nonminimally coupled massive Kalb–Ramond systems. Because the present calculation uses a nondynamical metric and studies only the linearized spectrum, it does not determine the perturbative-action properties of the modes.

A definitive comparison would require expanding the action beyond linear order about the nonzero Lorentz-breaking background and determining the kinetic structure, canonical degrees of freedom, and scale at which nonlinear interactions become important.

References

We therefore interpret the results above as classical linear instabilities of the fixed-background problem, while leaving their possible relation to strong coupling for future investigation.

— Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background  (2609.39936 - Lyu et al., 30 Sep 2026) in Section “Relation to strong coupling”