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

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 the nth-order theory of this type, we provide a general recipe 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.