Nonintegrability of self-dual Yang–Mills–Higgs system

Inami, Takeo; Minakami, Shie; Nitta, Muneto

doi:10.1016/j.nuclphysb.2006.06.015

Cited by 9 publications

(5 citation statements)

References 54 publications

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“…Non-integrability of this equation has been addressed recently in [120] by using the Painlevé test. in the strong gauge coupling limit g 2 → ∞, in which the model reduces to the HK nonlinear sigma model.…”

Section: Wall Solutions and Their Moduli Spacementioning

confidence: 99%

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Solitons in the Higgs phase: the moduli matrix approach

Eto

Isozumi

Nitta

et al. 2006

J. Phys. A: Math. Gen.

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We review our recent work on solitons in the Higgs phase. We use U (N C ) gauge theory with N F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories.Instanton-vortex systems, monopole-vortex-wall systems, and webs of walls in Abelian gauge theories are found to admit negative energy objects with the instanton charge (called intersectons), the monopole charge (called boojums) and the Hitchin charge, respectively.We characterize the total moduli space of these elementary as well as composite solitons. In particular the total moduli space of walls is given by the complex Grassmann manifold SU (N F )/[SU (N C ) × SU (N F − N C ) × U (1)] and is decomposed into various topological sectors corresponding to boundary condition specified by particular vacua. The moduli space of k vortices is also completely determined and is reformulated as the half ADHM construction. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices, and walls. Review parts contain our works on domain walls [1] (hep-th/0404198) [2] (hep-th/0405194) [3] (hep-th/0412024) [4] (hep-th/0503033) [5] (hep-th/0505136), vortices [6] (hep-th/0511088) [7] (hep-th/0601181), domain wall webs [8] (hep-th/0506135) [9] (hep-th/0508241) [10] (hep-th/0509127), monopolevortex-wall systems [11] (hep-th/0405129) [12] (hep-th/0501207), instanton-vortex systems [13] (hep-th/0412048), effective Lagrangian on walls and vortices [14] (hep-th/0602289), classification of BPS equations [15] (hep-th/0506257), and Skyrmions [16] (hep-th/0508130). † In this paper we keep terminology of "instantons" for Yang-Mills instantons in four Euclidean space. They become particles in 4+1 dimensions.

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Section: Wall Solutions and Their Moduli Spacementioning

confidence: 99%

“…Note that log Ω is regular everywhere while ξ is singular at vortex positions. Non-integrability of the master equation has been shown in [120].…”

Section: Vortex Solutions and Their Moduli Spacementioning

confidence: 99%

Solitons in the Higgs phase: the moduli matrix approach

Eto

Isozumi

Nitta

et al. 2006

J. Phys. A: Math. Gen.

Self Cite

385

565

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“…We call this equivalence relation as the V -equivalence relation and denote it as H 0 ∼ V H 0 . The master equation was shown to be non-integrable [44], and the existence and uniqueness of its solution for any given H 0 was rigorously proved at least for the U(1) gauge theory [20].…”

Section: Bps Equations and The Moduli Matrixmentioning

confidence: 99%

Domain walls with non-Abelian clouds

et al. 2008

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Domain walls in U(N) gauge theories, coupled to Higgs scalar fields with degenerate masses, are shown to possess normalizable non-Abelian Nambu-Goldstone(NG) modes, which we call non-Abelian clouds. We construct the moduli space metric and its Kähler potential of the effective field theory on the domain walls, by focusing on two models: a U(1) gauge theory with several charged Higgs fields, and a U(N) gauge theory with 2N Higgs fields in the fundamental representation. We find that non-Abelian clouds spread between two domain walls and that their rotation induces long-range repulsive force, in contrast to a U(1) mode in models with fully non-degenerate masses which gives short-range force. We also construct a bound state of dyonic domain walls by introducing the imaginary part of the Higgs masses. In the latter model we find that when all walls coincide SU(N) L × SU(N) R × U(1) symmetry is broken down to SU(N) V , and U(N) A NG modes and the same number of quasi-NG modes are localized on the wall. When n walls separate, off diagonal elements of U(n) NG modes have wave functions spreading between two separated walls (non-Abelian clouds), whereas some quasi-NG modes turn to NG bosons as a result of further symmetry breaking U(n) V → U(1) n V . In the case of 4 + 1 dimensional bulk, we can dualize the effective theory to the supersymmetric Freedman-Townsend model of non-Abelian 2-form fields.

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“…Non-Abelian vortices also play prominent roles as instantons in non-perturbative dynamics of gauge theories in lower dimensions, similar to the role of Yang-Mills instantons [13] in four dimensions; the non-perturbative partition function has been extensively studied by the vortex counting in N = (2, 2) supersymmetric gauge theories in two dimensions [14], similar to the instanton counting in four dimensions [15]. However, vortex equations are not integrable even in the BPS limit [16], and explicit solutions and the moduli space metric are not available. This is in contrast to the case of the self-dual equations for Yang-Mills instantons, for which the well-known Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction is available [17].…”

Section: Introductionmentioning

confidence: 99%

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

Eto

Fujimori

Nitta

et al. 2013

J. High Energ. Phys.

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We successfully exhaust the complete set of exact solutions of non-Abelian vortices in a quiver gauge theory, that is, the S[U (N ) × U (N )] gauge theory with a bi-fudamental scalar field on a hyperbolic plane with a certain curvature, from SO(3)-invariant SU (2N ) Yang-Mills instanton solutions. This work provides, for the first time, exact non-Abelian vortex solutions. We establish the ADHM construction for non-Abelian vortices and identify all the moduli parameters and the complete moduli space.

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Nonintegrability of self-dual Yang–Mills–Higgs system

Abstract: We examine integrability of self-dual Yang-Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painlevé property. This fact suggests that these equations are not integrable. *

Cited by 9 publications

References 54 publications

Solitons in the Higgs phase: the moduli matrix approach

Solitons in the Higgs phase: the moduli matrix approach

Domain walls with non-Abelian clouds

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

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