Local and semi-local vortices in the Yang–Mills–Chern–Simons model

Buck, Michel; Moreno, E.C.; Schaposnik, F

doi:10.1088/1751-8113/42/20/205401

Cited by 3 publications

(6 citation statements)

References 35 publications

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“…Thus we conclude that the moduli space of the topological solitons in the intermediate vacua is Refs. [22,23]. Here we first show that the semi-local vortices also exist in the model with N f = N.…”

Section: The U(2) Chern-simons Solitonsmentioning

confidence: 67%

“…These internal orientational modes are related to the color and flavor degrees of freedom, which make the solitons being truly of the NA kind. Soon after its discovery, the NA semi-local vortices were found in the U(N) CS theory with N f > N fundamental Higgs fields [22,23]. The dynamics of the NA vortices was studied in [24] and the NA vortices with a globally conserved charge was found in [25].…”

Section: Introductionmentioning

confidence: 99%

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Zero-modes of non-Abelian solitons in three-dimensional gauge theories

Eto

Gudnason

2011

J. Phys. A: Math. Theor.

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We study non-Abelian solitons of the Bogomol'nyi type in N = 2 (d = 2 + 1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons.We find that the zero-modes of the topological solitons are governed by the moduli matrix H 0 only and those of the non-topological solitons are governed by both H 0 and the gauge invariant field Ω. We prove local uniqueness of the master equation in the YM case and finally, compare all results between the in the early '90s and we shall refer to all these as solitons of the Abelian kind. 1The second era of the CS solitons recently started when a new type of the toplogical CS soliton of the non-Abelian (NA) kind 2 was found in the U(N) CS theory coupled with N Higgs fields in the fundamental representation [21]. The NA CS vortex found so far is quite similar to the NA YM vortex [17,18,19,20]. It lives in the color-flavor locked, broken vacuum (i.e. the Higgs vacuum) and has internal orientational zero-modes, CP N −1 . These internal orientational modes are related to the color and flavor degrees of freedom, which make the solitons being truly of the NA kind. Soon after its discovery, the NA semi-local vortices were found in the U(N) CS theory with N f > N fundamental Higgs fields [22,23]. The dynamics of the NA vortices was studied in Ref.[24] and the NA vortices with a globally conserved charge was found in Ref. [25].The topological solitons of both local, semi-local and fractional kind in the NA CS theory with an arbitrary gauge group of the form U(1) times a simple group have also been studied very recently in Refs. [26,27]. Thus, the study on the CS solitons is being revived now.The NA CS solitons found so far are all topological solitons in the broken vacuum (the Higgs vacuum). This is because their discovery [21] was inspired by the NA YM vortex which is indeed a topological soliton living in the broken (Higgs) vacuum. However, we know that there are also non-topological solitons in the Abelian CS models [7]. So it is natural to ask ourselves if nontopological or other solitons of the NA kind exist or not, in NA CS theories. With this question in mind, we will be concerned in this paper with vortices of all possible non-Abelian kinds in the NA CS gauge theories with the gauge group G being general; G = U(1) × G ′ with G ′ is an arbitrary simple group. As if it was not broad enough a spectrum, we will make every statement throughout the paper be independent of the gauge group. Beyond our naive expectation, we will find semi-local NA vortices of both topological and non-topological types in the models where the number of ...

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Section: The U(2) Chern-simons Solitonsmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Zero-modes of non-Abelian solitons in three-dimensional gauge theories

Eto

Gudnason

2011

J. Phys. A: Math. Theor.

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“…Furthermore, Refs. [59,60,61] have considered packaging together the Yang-Mills and the non-Abelian Chern-Simons terms for U(N) gauge groups. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical solutions were provided in Ref. [61] for the Yang-Mills-Chern-Simons U(N) theory and in Ref. [58] for the Chern-Simons U(N) theory and in both cases they have found that the semi-local moduli parameter, when non-zero, destroys the ring-like characteristic of the magnetic flux that the vortex solutions in Chern-Simons theories usually possess.…”

Section: Introductionmentioning

confidence: 99%

Fractional and semi-local non-Abelian Chern–Simons vortices

Gudnason¹

2010

Nuclear Physics B

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In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U (1) × SO(2M ) and G = U (1) × U Sp(2M ) theories. The master equations are solved numerically using appropriate Ansätze for the moduli matrix field. In the fractional case the vortices are solved in the transverse plane due to the broken axial symmetry of the configurations (i.e. they are non-rotational invariant). It is shown that unless the fractional vortex-centers are all coincident (i.e. local case) the ring-like flux structure, characteristic of Chern-Simons vortices, will become bell-like fluxes -just as those of the standard Yang-Mills vortices. The asymptotic profile functions are calculated in all cases and the effective size is identified.

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“…Furthermore Refs. [26,27,28] have considered packag-ing together the Yang-Mills and the non-Abelian Chern-Simons terms for U(N) gauge groups. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian Chern–Simons vortices with generic gauge groups

Gudnason

2009

Nuclear Physics B

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We study non-Abelian Chern-Simon BPS-saturated vortices enjoying N = 2 supersymmetry in d = 2 + 1 dimensions, with generic gauge groups of the form U (1) × G ′ , with G ′ being a simple group, allowing for orientational modes in the solutions. We will keep the group as general as possible and utilizing the powerful moduli matrix formalism to provide the moduli spaces of vortices and derive the corresponding master equations. Furthermore, we study numerically the vortices applying a radial Ansatz to solve the obtained master equations and we find especially a splitting of the magnetic fields, when the coupling constants for the trace-part and the traceless part of the Chern-Simons term are varied, such that the Abelian magnetic field density can become negative near the origin of the vortex while the non-Abelian part stays positive, and vice versa.

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Local and semi-local vortices in the Yang–Mills–Chern–Simons model

Cited by 3 publications

References 35 publications

Zero-modes of non-Abelian solitons in three-dimensional gauge theories

Zero-modes of non-Abelian solitons in three-dimensional gauge theories

Fractional and semi-local non-Abelian Chern–Simons vortices

Non-Abelian Chern–Simons vortices with generic gauge groups

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