Higher derivative extensions of $3d$ Chern-Simons models: conservation laws and stability

TL;DR

This paper explores higher derivative 3D vector field models based on polynomial Chern-Simons operators, identifying conserved tensors that ensure classical stability for specific parameter choices.

Contribution

It introduces a general method for constructing conserved tensors in higher derivative 3D models, including bounded tensors that guarantee classical stability.

Findings

Existence of bounded conserved tensors for certain parameters

Construction of stable interacting models

Explicit examples of stable higher derivative theories

Abstract

We consider the class of higher derivative $3d$ vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For $n$-th order theory of this type, we provide a general receipt for constructing $n$-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.