# Stable interactions between higher derivative extended Chern-Simons and charged scalar field

## TL;DR

This paper explores the interactions between higher derivative extended Chern-Simons theories and charged scalar fields, revealing a parameterized family of non-Lagrangian interactions that can preserve stability through conserved tensors.

## Contribution

It introduces a new class of non-Lagrangian interactions between extended Chern-Simons and charged scalars, characterized by a multi-parameter series that can ensure stability.

## Key findings

- Interactions form an (N+n)-parameter series.
- Conserved second-rank tensor can bound energy.
- Stability depends on boundedness of the tensor's 00-component.

## Abstract

We consider inclusion of interactions between the higher derivative extended Chern-Simons and charged scalar field. We demonstrate that the order $N$ extended Chern-Simons and order $2n$ charged scalar admit the $(N+n)$-parameter series of interaction vertices. The interactions are in general non-Lagrangian, but they preserve a certain conserved second-rank tensor, whose parameters are determined by the coupling. The $00$-component of this tensor can be bounded even if the canonical energy of the model is unbounded before the inclusion of interaction. If the $00$-component of conserved tensor is bounded, the theory is stable.