Driving Operators Relevant: A Feature of Chern-Simons Interaction

Abstract

By computing anomalous dimensions of gauge invariant composite operators $(\bar{\psi }\psi {)}^n$ and $({\varphi }^{\ast }\varphi {)}^n$ in Chern-Simons fermion and boson models, we address that Chern-Simons interactions make these operators more relevant or less irrelevant in the low energy region. We obtain a critical Chern-Simons fermion coupling, $\frac{1}{{\kappa }_c^2}=\frac{6}{19}$, for a phase transition at which the leading irrelevant four-fermion operator $(\bar{\psi }\psi {)}^2$ becomes marginal, and a critical Chern-Simons boson coupling, $\frac{1}{{\kappa }_c^2}=\frac{6}{34}$, for a similar phase transition for the leading irrelevant operator $({\varphi }^{\ast }\varphi {)}^4$. We see this phenomenon also in the $1/N$ expansion.

(ten pages, latex, figures included)

References in corpus (2)

• Mott Transition in An Anyon Gas
• Two-Loop Analysis of Non-abelian Chern-Simons Theory

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• Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study
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• Supplementary Information for: 'Spontaneous Skyrmion Ground States in Magnetic Metals'
• On spin-1 massive particles coupled to a Chern-Simons field