Extended Chern-Simons model for a vector multiplet

Abstract

We consider a gauge theory of vector fields in $3d$ Minkowski space. At the free level, the dynamical variables are subjected to the extended Chern-Simons (ECS) equations with higher derivatives. If the color index takes $n$ values, the third-order model admits a $2n$-parameter series of second-rank conserved tensors, which includes the canonical energy-momentum. Even though the canonical energy is unbounded, the other representatives in the series can have bounded from below $00$-component. The theory admits consistent self-interactions with the Yang-Mills gauge symmetry. The Lagrangian couplings preserve the unbounded from below energy-momentum tensor, and they do not lead to a stable non-linear theory. The non-Lagrangian couplings are consistent with the existence of conserved tensor with a bounded from below $00$-component. These models are stable at the non-linear level. The dynamics of interacting theory admits a constraint Hamiltonian form. The Hamiltonian density is given by the $00$-component of the conserved tensor. In the case of stable interactions, the Poisson bracket and Hamiltonian do not follow from the canonical Ostrogradski construction. The particular attention is paid to the "triply massless" ECS theory, which demonstrates instability already at the free level. It is shown that the introduction of extra scalar field, serving as Higgs, can stabilize dynamics in the vicinity of the local minimum of energy. The equations of motion of stable model are non-Lagrangian, but they admit the Hamiltonian form of dynamics with a bounded from below Hamiltonian.

arXiv comment34 pages

References in corpus (26)

• f(R) Theories Of Gravity
• Local BRST cohomology in gauge theories
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Benign vs malicious ghosts in higher-derivative theories
• Conformal Gravity and Extensions of Critical Gravity
• Metastability in Quadratic Gravity
• Lagrange structure and quantization
• Higher Derivative Chern--Simons Extensions
• The Projective Unitary Irreducible Representations of the Poincaré Group in 1+2 Dimensions
• A Hamiltonian Formulation of the Pais-Uhlenbeck Oscillator that Yields a Stable and Unitary Quantum System
• Hamiltonian analysis of curvature-squared gravity with or without conformal invariance
• Rigid Symmetries and Conservation Laws in Non-Lagrangian Field Theory
• Higher Derivative Scalar Quantum Field Theory in Curved Spacetime
• Stable interactions in higher derivative field theories of derived type
• Remarks on quantization of Pais-Uhlenbeck oscillators
• Reduction of order and Fadeev-Jackiw formalism in generalized electrodynamics
• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• BRST analysis of general mechanical systems
• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
• Stable interactions via proper deformations
• Hamiltonian structures for Pais-Uhlenbeck oscillator
• Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions
• Resonance and stability of higher derivative theories of derived type
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• On the canonical formalism of $f(R)$-type gravity using Lie derivatives
• Free Fields for Any Spin in 1+2 Dimensions