Abstract
Within the superfield formalism, we study the renormalization group improvement of the effective superpotential for the ${\cal N}=2$ Chern-Simons-matter theory, explicitly obtain the improved effective potential and discuss the minima of the effective potential and a problem of mass generation in the theory.
Highlights
The effective potential is known to be one of the central objects of quantum field theory allowing one to obtain information about low-energy effective dynamics of a theory, spontaneous symmetry breaking, mass generation, and other related issues [1]
Within the superfield formalism, we study the renormalization group improvement of the effective superpotential for the N 1⁄4 2 Chern-Simons-matter theory, explicitly obtain the improved effective potential and discuss the minima of the effective potential and a problem of mass generation in the theory
Its key idea is as follows: we start with the beta functions which in three-dimensional theories began to be contributed at two loops, and solve the corresponding renormalization group equations taking into account that they must be satisfied by the complete effective potential composed by all-loop contributions
Summary
The effective potential is known to be one of the central objects of quantum field theory allowing one to obtain information about low-energy effective dynamics of a theory, spontaneous symmetry breaking, mass generation, and other related issues [1]. Its key idea is as follows: we start with the beta functions which in three-dimensional theories began to be contributed at two loops, and solve the corresponding renormalization group equations taking into account that they must be satisfied by the complete effective potential composed by all-loop contributions. The Wess-Zumino model possesses nontrivial beta function βðλÞ and anomalous dimension γΦ renormalization group functions, see e.g., [20]; the effective superpotential can be evaluated once Veff have to satisfy the RGE (8). In order to study the properties of the vacuum, let us write the effective potential Ueff in terms of the component fields It is obtained through integrating of Veff over the Grassmannian variable like in (7). The corresponding gauge fixing and Faddeev-Popov actions are given by
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