Renormalization group study of the Chern-Simons field coupled to scalar matter in a modified BPHZ subtraction scheme

Albuquerque, Luiz C. de; Gomes, M.; Silva, A. J. da

doi:10.1103/physrevd.62.085005

Cited by 10 publications

(15 citation statements)

References 35 publications

(66 reference statements)

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“…confirming the results obtained in [5] by using soft BPHZ [4] and also in [7] by using dimensional reduction. These results are also in qualitative agreement with that of [8] but, differently of what happens with the effective potential, disagree with those of [14] (which in our notation are γ ϕ = 0 and β ν = 7 4π 2 ν 2 ) where dimensional regularization with minimal subtraction was used.…”

Section: Renormalization Group Analysissupporting

confidence: 86%

Dynamical breakdown of symmetry in a (2+1)-dimensional model containing the Chern-Simons field

2004

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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.

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Section: Renormalization Group Analysissupporting

confidence: 86%

Dynamical breakdown of symmetry in a (2+1)-dimensional model containing the Chern-Simons field

2004

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“…Now, studying a possible minimum of such a Kählerian effective superpotential for v Þ 0, we found that e 2 % ð4:7 Â 10 À2 Þe 6 , which implies e $ 2. Thus, as in other four-and three-dimensional scalar models [1][2][3][4][5][6], in this case the Coleman-Weinberg effect is not feasible, because for N ¼ 2 the model presents only one coupling constant into play. Our results are in agreement with previous results obtained by Gaiotto and Yin [20] and Buchbinder et al [21,34], where it was shown that the N ¼ 2, 3 SCSM does not exhibit spontaneous breaking of superconformal invariance.…”

Section: Extended Susy Modelmentioning

confidence: 94%

“…The same happens in the supersymmetric Maxwell theory [17], and nonsupersymmetric three-dimensional gauge models [2][3][4][5][6]. Now, we evaluate the two-loop contributions to the tadpole equation, which arise from the diagrams depicted in Fig.…”

Section: The Supersymmetric D ¼ ð2 þ 1þ Chern-simons-matter Modelmentioning

confidence: 96%

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Coleman-Weinberg mechanism in a three-dimensional supersymmetric Chern-Simons-matter model

et al. 2010

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Using the superfield formalism, we study the dynamical breaking of gauge symmetry and superconformal invariance in the N ¼ 1 three-dimensional supersymmetric Chern-Simons model, coupled to a complex scalar superfield with a quartic self-coupling. This is an analogue of the conformally invariant Coleman-Weinberg model in four spacetime dimensions. We show that a mass for the gauge and matter superfields are dynamically generated after two-loop corrections to the effective superpotential. We also discuss the N ¼ 2 extension of our work, showing that the Coleman-Weinberg mechanism in such model is not feasible, because it is incompatible with perturbation theory.

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“…In this case, however, dynamical symmetry breaking appears only at two loops [17,18,19,20], and not at the one loop level, as in four dimensions.…”

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confidence: 87%

Spontaneous gauge symmetry breaking in a supersymmetric Chern-Simons model

et al. 2007

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This works presents a perturbative analysis of the supersymmetric Chern-Simons model in three spacetime dimensions coupled to a Higgs field, using the superfield formalism. We study the spontaneous symmetry breaking of the U (1) gauge symmetry and evaluate the first quantum corrections to the effective action in the broken phase. We show that the infinite renormalization of the gap equation is enough to ensure the renormalizability of the model at the first loop level.PACS numbers: 1.15. Ex, 11.10.Gh,11.30.Pb,12.60.Jv Field theories in three-dimensional spacetime are often simpler than their similar four dimensional counterparts and, as such, can be regarded as useful laboratories for several field theoretical properties. In particular, induced by the Chern-Simons term [1, 2], three dimensional theories exhibit massive gauge fields, exotic statistics and fractional spin, relevant qualities for the study of the quantized Hall effect [3]. In the non-Abelian case, the invariance of the action under large gauge transformations requires the Chern-Simons coefficient to be quantized [1], an aspect that can be explicitly verified in perturbation theory [4,5].One interesting possibility that has been considered in the literature is the coupling of the ChernSimons term to a Higgs field (CSH), thus allowing for spontaneous gauge symmetry breaking to occur, and a nontrivial dynamics for the Chern-Simons gauge field to be settled (giving rise to a self-dual model, which happens to be equivalent to a Maxwell-Chern-Simons theory [6]). The quantization of the Chern-Simons coefficient for non-Abelian theories in the broken phase holds if the remaining gauge symmetry is non-Abelian [7,8], whereas such quantization does not happen in the case of an Abelian theory, or a completely broken non-Abelian gauge symmetry [9,10,11]. Also, for a specific form of the Higgs potential, the CSH model has solutions which satisfy a Bogomol'nyi equation [12,13]. The exact form of this potential can be obtained either by imposing a self-dual condition on the matter field [14] or by enlarging the model to obtain an N = 2 supersymmetric theory [15]. It is interesting to note that a tridimensional analog of the Coleman-Weinberg model in * Electronic address: lehum, alysson, mgomes, ajsilva@fma.if.usp.br

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Renormalization group study of the Chern-Simons field coupled to scalar matter in a modified BPHZ subtraction scheme

Cited by 10 publications

References 35 publications

Dynamical breakdown of symmetry in a (2+1)-dimensional model containing the Chern-Simons field

Dynamical breakdown of symmetry in a (2+1)-dimensional model containing the Chern-Simons field

Coleman-Weinberg mechanism in a three-dimensional supersymmetric Chern-Simons-matter model

Spontaneous gauge symmetry breaking in a supersymmetric Chern-Simons model

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