The Perturbative Gross Neveu Model Coupled to a Chern-Simons Field: A Renormalization Group Study
V. S. Alves, M. Gomes, S. V. L. Pinheiro, A. J. da Silva
TL;DR
This paper investigates how a Chern-Simons field influences the perturbative behavior of a Gross Neveu model in 2+1 dimensions, revealing that the Chern-Simons coupling reduces the dimension of certain operators.
Contribution
It provides a renormalization group analysis of the Gross Neveu model coupled to a Chern-Simons field, highlighting the impact on operator dimensions in low-momentum regimes.
Findings
Operator dimensions decrease with increasing Chern-Simons coupling.
The study confirms the effect using dimensional renormalization techniques.
Results are specific to the one-fermion case in 2+1 dimensions.
Abstract
In 2+1 dimensions, for low momenta, using dimensional renormalization we study the effect of a Chern-Simons field on the perturbative expansion of fermions self interacting through a Gross Neveu coupling. For the case of just one fermion field, we verify that the dimension of operators of canonical dimension lower than three decreases as a function of the Chern-Simons coupling.
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