Renormalization group and conformal symmetry breaking in the Chern-Simons theory coupled to matter

Journal Article · Fri Oct 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.085006· OSTI ID:21432409

Dias, A G; Ferrari, A F ^[1]

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1. Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Rua Santa Adelia, 166, 09210-170, Santo Andre, SP (Brazil)

The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved effective potential computation based on two-loop calculations and the renormalization group equation: The latter allows us to sum up series of terms in the effective potential where the power of the logarithms are one, two, and three units smaller than the total power of coupling constants (i.e., leading, next-to-leading, and next-to-next-to-leading logarithms). For the sake of this computation we determined the beta function of the fermion-fermion-scalar-scalar interaction and the anomalous dimension of the scalar field. We show that the improved effective potential provides a much more precise determination of the properties of the theory in the broken phase, compared to the standard effective potential obtained directly from the loop calculations. This happens because the region of the parameter space where dynamical symmetry breaking occurs is drastically reduced by the improvement discussed here.

• OSTI ID: 21432409
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANOMALOUS DIMENSION
BREAKDOWN
CALCULATION METHODS
CONFORMAL INVARIANCE
COUPLING CONSTANTS
EQUATIONS
FERMIONS
FIELD THEORIES
INTERACTIONS
INVARIANCE PRINCIPLES
MATTER
QUANTUM FIELD THEORY
RENORMALIZATION
SCALAR FIELDS
SCALE DIMENSION
STABILITY
SYMMETRY BREAKING
THREE-DIMENSIONAL CALCULATIONS