Renormalization group study of anyon superconductivity

Grigoryev, G.V.; Kazakov, D. I.

doi:10.1016/0370-2693(91)91742-e

Cited by 7 publications

(11 citation statements)

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“…3 Renormalization group and finite temperature properties of this N = 2 supersymmetric theory has been studied. 4 It is well known that a theory with extended supersymmetry has less ultraviolet divergence. Some supersymmetric theories have been shown to be even finite.…”

Section: Introductionmentioning

confidence: 99%

Self-dual Chern-Simons Higgs systems with anN=3extended supersymmetry

Kao

Lee

1992

Phys. Rev. D

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Section: Introductionmentioning

confidence: 99%

Self-dual Chern-Simons Higgs systems with anN=3extended supersymmetry

Kao

Lee

1992

Phys. Rev. D

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“…The b functions for the dimensionless couplings e, a, b, h, and h and the dimensionful parameters q and M are not affected by QD to the order considered here, and their corresponding expressions, which are somewhat lengthy, can be found in [10]. The fixed points correspond to the zeros of the b functions for the dimensionless couplings.…”

Section: Infrared Stable Supersymmetry In Chern-simons Theories With mentioning

confidence: 77%

“…Our notation and conventions are those of [10,11]. The matter fields are in the fundamental representation of the global SU͑N͒ symmetry group (j, k 1, .…”

Section: Infrared Stable Supersymmetry In Chern-simons Theories With mentioning

confidence: 99%

“…The anomalous dimension at the critical point g ‫ء‬ can be computed by using the RG equations for the Abelian CS theory without QD [10] and vanishes as g ! g ‫ء‬ in the IR limit.…”

Section: Infrared Stable Supersymmetry In Chern-simons Theories With mentioning

confidence: 99%

“…Although the CS gauge coupling remains unrenormalized as before, the matter couplings require renormalization. This leads to non-vanishing β-functions exhibiting a complicated and non-trivial renormalization group (RG) flow and a rich set of fixed points [10]. By analyzing the CS gauge theory with matter couplings in the infrared (IR) limit the authors of Ref.…”

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Infrared Stable Supersymmetry in Chern-Simons Theories with Matter and Quenched Disorder

Hamidian

1998

Phys. Rev. Lett.

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We study Abelian Chern-Simons field theories with matter fields and global SU͑N͒ symmetry in the presence of random weak quenched disorder. In the absence of disorder, these theories possess N 2 supersymmetric fixed points and N 1 supersymmetric fixed lines in the infrared limit. We show that, although the presence of disorder forbids any supersymmetry of the bare action, infrared stable supersymmetric fixed points and fixed lines are realized in the disorder-averaged effective theories. [S0031-9007(98)05317-4] Model systems in less than four (space-time) dimensions have often played an important role in understanding general methods and applications of quantum field theory and developing ideas in four dimensions.Notable among these are Chern-Simons (CS) gauge field theories in (2 1 1) dimensions [1], which have a long history and have been intensively studied in recent years. There are several motivations for studying CS theories. From a purely theoretical and mathematical point of view, they constitute a new class of (topological) gauge theories and are closely related to certain models in topological quantum field theory [2] in three spacetime dimensions and integrable statistical mechanical models and rational conformal field theories in two dimensions [3]. From the more physical point of view, there has been general interest in CS theories due to their resemblance to the high-temperature limit of (3 1 1) dimensional gauge theories and their possible relevance to certain condensed matter phenomena, in particular high-T C superconductivity [4] and the quantum Hall effect [5].Although CS gauge theories are in many respects similar to their four-dimensional counterparts, there are substantial differences which are intimately connected with the appearance of the CS three-form in the action [6] and parity anomalies [7]. Formally, CS gauge theories are strictly renormalizable quantum field theories and their perturbative expansions contain logarithmic divergences. However, contrary to the Yang-Mills and Maxwell gauge theories, and due to their topological nature, infinite charge renormalizations are absent in both Abelian and non-Abelian CS gauge theories [8,9].The situation changes significantly when matter fields are added to the CS theory. Although the CS gauge coupling remains unrenormalized as before, the matter couplings require renormalization. This leads to nonvanishing b functions exhibiting a complicated and nontrivial renormalization group (RG) flow and a rich set of fixed points [10]. By analyzing the CS gauge theory with matter couplings in the infrared (IR) limit, the authors of Ref.[10] were able to show that, quite unexpectedly, some of the resulting fixed points and fixed lines exhibit N 1 and N 2 supersymmetry, which are realized as IR stable or saddle point solutions of the corresponding RG equations.In this Letter, we study Abelian CS field theories with matter in the presence of random weak quenched disorder (QD) at zero temperature. The model is described by the (Euclidean) action

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1995

Lecture Notes in Physics Monographs

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Renormalization group study of anyon superconductivity

Cited by 7 publications

References 23 publications

Self-dual Chern-Simons Higgs systems with anN=3extended supersymmetry

Self-dual Chern-Simons Higgs systems with anN=3extended supersymmetry

Infrared Stable Supersymmetry in Chern-Simons Theories with Matter and Quenched Disorder

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