Vortices on the higgs branch of the Seiberg–Witten theory

Yung, A.

doi:10.1016/s0550-3213(99)00529-5

Cited by 37 publications

(70 citation statements)

References 29 publications

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“…Note, that the logarithmic suppression of the string tension is not specific for non-Abelian strings. Similar expression was found for the ANO string on a Higgs branch [26,27].…”

Section: String Profile Functionssupporting

confidence: 77%

“…In many instances this breaking provides topological reasons behind formation of vortex strings. A dynamical side of the problem of the vortex string formation in theories with Higgs branches was addressed in [25,26,27]. A priori it is not clear at all whether or not stable string solutions exist in this class of theories.…”

Section: String Profile Functionsmentioning

confidence: 99%

“…In particular, it was shown in [25] that infinitely long strings cannot be formed in this case due to infrared divergences. Later this problem was studied in [26,27]. It was shown that vortices on Higgs branches become logarithmically "thick" due to the presence of massless scalars in the bulk.…”

Section: String Profile Functionsmentioning

confidence: 99%

“…Still, they are well defined if IR divergences are regularized. One way of regularization is to consider a vortex string of the finite length L [26]. This setup is typical for the confinement problem.…”

Section: String Profile Functionsmentioning

confidence: 99%

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Non-Abelian strings in N=1 supersymmetric QCD

Ievlev

Yung

2017

Phys. Rev. D

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Non-Abelian flux tubes (strings) are well studied in N = 2 supersymmetric QCD in (3+1) dimensions. In addition to translational zero modes they have also orientational moduli associated with rotations of their fluxes inside a nonAbelian group. The dynamics of the orientational moduli is described by the two dimensional CP(N − 1) model living on the world sheet of the non-Abelian string. In this paper we consider a deformation of N = 2 supersymmetric QCD with the U(N ) gauge group and N f = N quark flavors with a mass term µ of the adjoint matter. In the limit of large µ the theory flows to an N = 1 supersymmetric QCD. We study the solution for the non-Abelian string in this limit and derive an effective theory on the string world sheet. The bosonic sector of this theory is still given by the CP(N −1) model but its scale is exponentially small as compared to the scale of the four dimensional bulk theory in contrast to the N = 2 case where these scales are equal. We study also the fermionic sector of the world sheet theory. Upon the deformation the non-Abelian string is no longer BPS and we show that the fermionic superorientational zero modes are all lifted. This leaves us with the pure bosonic CP(N − 1) model on the string world sheet in the limit of N = 1 QCD. We also discuss what happens to confined monopoles at large µ.

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“…Note, that the logarithmic suppression of the string tension is not specific for non-Abelian strings. Similar expression was found for the ANO string on a Higgs branch [26,27].…”

Section: String Profile Functionssupporting

confidence: 77%

Section: String Profile Functionsmentioning

confidence: 99%

Section: String Profile Functionsmentioning

confidence: 99%

Section: String Profile Functionsmentioning

confidence: 99%

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Non-Abelian strings in N=1 supersymmetric QCD

Ievlev

Yung

2017

Phys. Rev. D

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“…given in equation (14). Since the absolute phases of m i are not fixed, it has the topology of a torus of genus g = N − 1.…”

Section: Infrared Dynamics At Maximal Singularitiesmentioning

confidence: 99%

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

et al. 2000

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We study the electric flux tubes that undertake color confinement in N = 2 supersymmetric Yang-Mills theories softly broken down to N = 1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U (1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.

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Two species of vortices in massive gauged non-linear sigma models

Izquierdo

Fuertes

Guilarte

2015

J. High Energ. Phys.

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Non-linear sigma models with scalar fields taking values on CP n complex manifolds are addressed. In the simplest n = 1 case, where the target manifold is the S 2 sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the selfdual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2 + 1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged CP 2 model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1) × SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged CP N models.

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Vortices on the higgs branch of the Seiberg–Witten theory

Cited by 37 publications

References 29 publications

Non-Abelian strings in N=1 supersymmetric QCD

Non-Abelian strings in N=1 supersymmetric QCD

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

Two species of vortices in massive gauged non-linear sigma models

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