Dynamical Breakdown of Symmetry in a (2+1) Dimensional Model Containing the Chern-Simons Field

TL;DR

This paper investigates how quantum effects induce symmetry breaking and mass generation in a (2+1)D model with scalar, fermionic, and Chern-Simons fields, revealing dynamical symmetry breakdown at two-loop level.

Contribution

It demonstrates dynamical symmetry breaking and mass generation in a (2+1)D Chern-Simons coupled model using two-loop effective potential calculations.

Findings

Symmetry is dynamically broken at two-loop order.

Masses for boson and fermion fields are generated.

Vacuum becomes asymmetric due to quantum corrections.

Abstract

We study the vacuum stability of a model of massless scalar and fermionic fields minimally coupled to a Chern-Simons field. The classical Lagrangian only involves dimensionless parameters, and the model can be thought as a (2+1) dimensional analog of the Coleman-Weinberg model. By calculating the effective potential, we show that dynamical symmetry breakdown occurs in the two-loop approximation. The vacuum becomes asymmetric and mass generation, for the boson and fermion fields takes place. Renormalization group arguments are used to clarify some aspects of the solution.