All exact solutions of non-Abelian vortices from Yang-Mills instantons

Eto, Minoru; Fujimori, Toshiaki; Nitta, Muneto; Ohashi, Keisuke

doi:10.1007/jhep07(2013)034

Cited by 6 publications

(7 citation statements)

References 50 publications

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“…As for the "magnetic fields" felt by these W bosons, it is clear that W ±(ℓ) is coupled to F (ℓ) 12 only, and W ±(r) to F (r) 12 only, as they arise from the original Yang-Mills action. Working out the coupling of W ±(ℓ) , as in [1], and similarly for W ±(r) , one finds the magnetic fields…”

Section: Vortex Zeromodesmentioning

confidence: 99%

“…The second purpose of this work is to discuss what appears to be a surprising contrast and a sort of complementarity existing between the physics of g r = 0 and g r = 0 systems, where g r is the SU r (N) coupling constant. In the former case one has nonAbelian vortex with fluctuating, quantum CP N −1 dynamics on the 2D string 1 Analytic vortex solutions are however known in certain systems defined on hyperbolic spaces with tuned curvature [10]- [12]. For relation to nonAbelian vortices and large winding see for example [11].…”

Section: Introductionmentioning

confidence: 99%

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NonAbelian vortices, large winding limits and Aharonov-Bohm effects

Bolognesi

Chatterjee

Konishi

2015

J. High Energ. Phys.

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Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U 0 (1) × SU ℓ (N ) × SU r (N ) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N ) ℓ+r . The presence of the massless SU(N ) ℓ+r gauge fields in 4D bulk introduces all sorts of nonlocal, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU r (N ) group (g r = 0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant g r is turned on.

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Section: Vortex Zeromodesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

NonAbelian vortices, large winding limits and Aharonov-Bohm effects

Bolognesi

Chatterjee

Konishi

2015

J. High Energ. Phys.

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“…For the Lifshitz-type non-linear sigma models, we have focused on Weyl rescaling and the coset space dimensional reduction have been used to map the instantons to Abelian vortices in the anisotropic system on the hyperbolic plane. As in the case of the instantons in four dimensions [58,59], it is also interesting to consider more general dimensional reductions which give non-Abelian theories in the two-dimensional spacetime and non-Abelian vortices in such theories.…”

Section: Summary and Discussionmentioning

confidence: 99%

Instantons in Lifshitz field theories

Fujimori

Nitta

2015

J. High Energ. Phys.

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BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.

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“…In flat space, their characteristic features can be understood from symmetry, since the bosonic theory admitting BPS vortices can be embedded into supersymmetric theory and BPS vortices preserve half of supercharges [3]. Important generalizations of BPS vortices have been studied in curved space, such as hyperbolic space [4,5,6,7] and general Riemann surfaces [8]. The moduli space of BPS vortices allows interesting applications to many physical phenomena, including the thermodynamics of vortices [9,10].…”

Section: Introductionmentioning

confidence: 99%

Higgs and Coulomb branch descriptions of the volume of the vortex moduli space

Ohta

Sakai

2019

Progress of Theoretical and Experimental Physics

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BPS vortex systems on closed Riemann surfaces with arbitrary genus are embedded into two-dimensional supersymmetric Yang-Mills theory with matters. We turn on background R-gauge fields to keep half of rigid supersymmetry (topological A-twist) on the curved space. We consider two complementary descriptions; Higgs and Coulomb branches. The path integral reduces to the zero mode integral by the localization in the Higgs branch. The integral over the bosonic zero modes directly gives an integral over the volume form of the moduli space, whereas the fermionic zero modes are compensated by an appropriate operator insertion. In the Coulomb branch description with the same operator insertion, the path integral reduces to a finite-dimensional residue integral. The operator insertion automatically determines a choice of integral contours, leading to the Jeffrey-Kirwan residue formula. This result ensures the existence of the solution to the BPS vortex equation and explains the Bradlow bounds of the BPS vortex. We also discuss a generating function of the volume of the vortex moduli space and show a reduction of the moduli space from semi-local to local vortices.

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All exact solutions of non-Abelian vortices from Yang-Mills instantons

Cited by 6 publications

References 50 publications

NonAbelian vortices, large winding limits and Aharonov-Bohm effects

NonAbelian vortices, large winding limits and Aharonov-Bohm effects

Instantons in Lifshitz field theories

Higgs and Coulomb branch descriptions of the volume of the vortex moduli space

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