BRST deformations and stability in the higher derivative Chern–Simons gauge theory

Abstract

We show the procedure of BRST deformations of the free Chern–Simons gauge theory with the higher derivatives in antifield formalism and obtain the consistent interactions in the master action at different orders. The key ingredient in our analysis is the local BRST-cohomology which plays a crucial role in the determination of the first-order deformation, also the Jacobi identity is needed since it will greatly simplify the calculations for us. Making using of the Dirac’s method, we give a detailed Hamiltonian analysis both for the free and interacting systems and exhibit that the number of physical degrees of freedom is unchanged after the deformation process. Moreover, we demonstrate that the free higher derivative system can be stabilized from the viewpoint of the existence of another bounded conserved quantities which are different from the canonical energy.

Extended Chern-Simons model for a vector multiplet

“…The Lagrangian interaction vertex (17) does not meet stability requirements. This confirms the instability of the variational coupling proposed in [42]. The stable interactions in the class of models ( 16) are inevitably non-Lagrangian.…”

“…The theory is stable if all the nonzero roots of characteristic polynomial are real and different and zero root has multiplicity one or two. The stability of the ECS theory is confirmed in work [42]. The ECS model has been shown to be a multi-Hamiltonian at the free level in [43].…”

“…This action functional was first derived in [42]. 5 The same paper tells us that the ( 17) is the most general form of consistent self-interactions in the gauge theory of vector fields.…”

“…It has been shown that the Yang-Mills vertex is unique in the covariant setting. The Lagrangian self-interactions of the gauge vector multiplet subjected to the ECS equations at free level has been reconsidered in article [42].…”

“…Depending on the values of coupling constants, it can be bounded or unbounded. The Lagrangian interaction vertex of the article [42] is unstable. The non-Lagrangian coupling can be consistent with the existence of bounded conserved tensor.…”