Intrinsically-defined higher-derivative Carrollian scalar field theories without Ostrogradsky instability

TL;DR

This paper develops a general class of higher-derivative scalar field theories on Carrollian manifolds, showing they have richer solutions and are more stable against Ostrogradsky instabilities compared to Lorentzian theories.

Contribution

It introduces the most general intrinsic Carrollian higher-derivative scalar theories and demonstrates their enhanced solution space and stability properties.

Findings

Solutions include massless particles with variable speeds.

Theories exhibit interference solutions not possible in Lorentzian settings.

Ostrogradsky instabilities can be mitigated by tuning coupling constants.

Abstract

We derive the most generic Carrollian higher derivative free scalar field theory intrinsically on a Carrollian manifold. The solutions to these theories are massless free particles propagating with speeds depending on the coupling constants in the Lagrangian, thus, allowing interference solutions which are not allowed on a Lorentzian manifold. This demonstrates that the set of solutions to the Carrollian theories is much larger than that of their Lorentzian counterparts. We also show that Carrollian higher derivative theories are more resistant to Ostrogradsky's instabilities. These instabilities can be resolved by choosing the coupling constants appropriately in the Carrollian Lagrangian, something that was proven to be impossible in Lorentzian theories.