Moduli Space of Non-Abelian Vortices

Keisuke Ohashi; Minoru Eto; Muneto Nitta; Norisuke Sakai; Youichi Isozumi

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Moduli Space of Non-Abelian Vortices

Minoru Eto, Youichi Isozumi, Muneto Nitta, Keisuke Ohashi, Norisuke Sakai

High Energy Physics - Theory · Submitted 8 Nov 2005

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The authors' main claim We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation.

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arXiv IDhep-th/0511088 (version 3)

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CitationKeisuke Ohashi, Minoru Eto, Muneto Nitta, Norisuke Sakai, Youichi Isozumi. "Moduli Space of Non-Abelian Vortices." arXiv:hep-th/0511088 (2005). https://pith.science/paper/VTPKDTW6

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We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (C x CP^{N-1})^k / S_k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. Relation to Kahler quotient construction is discussed.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation.	contribution 0.60	0.94	0.85	asserted 1.00
s1	Its open subset for separated vortices is found as the symmetric product (C x CP^{N-1})^k / S_k.	result 0.99	0.91	0.18	asserted 1.00
s2	Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold.	result 0.78	0.81	0.15	asserted 1.00
s3	Relation to Kahler quotient construction is discussed.	contribution 0.56	0.61	0.03	asserted 0.63

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Original abstract

We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (C x CP^{N-1})^k / S_k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. Relation to Kahler quotient construction is discussed.

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77 later papers cite it

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2 papers by the same authors are listed below: 1 built on it and 1 used its method or tool.

Builds on it 1 of 2 papers with this label · 1 by the same authors

By the same authors

Extended the moduli matrix formalism of this paper to include the extra adjoint field possessed by YMCSH theory, finding a result consistent with the index theorem calculation.

The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory (2021) (same authors) · 0.87 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 of 12 papers with this label · 1 by the same authors

By the same authors

Applied the moduli matrix for the vortex system of this paper to solve the first of the BPS equations.

Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories (2010) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

67 arXiv papers cite this in 127 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 81 sentences without a confident label

Builds on it 2 papers

[ref] ) to include the extra adjoint field that is possessed by YMCSH theory and the result is consistent with the result of the index theorem calculation, that the moduli are all contained in the moduli matrix, that comes from the self-dual BPS equation.

The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory · Conclusion and discussion · 0.87
We have generalized the moduli matrix formalism [ref] to clarify all possible moduli parameters of the minimally quantized fractional vortices.

Fractional Vortices and Lumps · Conclusion · 0.80

Uses its method or tool 11 papers

Let us apply the moduli matrix for the vortex system [ref] in order to solve the first of the BPS equations ([ref]) and ([ref]) (which is the same in both the YM and CS theories): H = S^-1H_0(z) , A̅ = -iS^-1S , S ∈G^ℂ ,

Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories · The moduli matrix method · 0.98
In this paper we apply the moduli matrix approach to study the vortex moduli space [ref] .

Vortex counting from field theory · Introduction · 1.00
The matter part of the above vortex equation can be solved by the moduli matrix $H_0(z)$ which is a color-flavor mixed matrix whose elements are holomorphic (polynomials) in $z$, for the left-handed vortex solution Eq. ([ref]) [ref] H = S^-1 H_0 (z) , W̅ = - i S^-1S , where $S$ is an element of the complex extension of the gauge group S(z,z̅)= e^ i ∑_I Λ^I(z,z̅) T^I ∈G^ℂ , Λ^I(z,z̅) ∈ℂ .

Fractional Vortices and Lumps · General arguments · 0.93

Compares with it 2 papers

In this respect, the present model (i.e. the model of [ref] ), where the $SU(N)×U(1)$ theory arises as a low-energy approximation of a spontaneously broken $SU(N+1)$ theory, differs essentially from the genuine $U(N)$ model studied by other groups [ref] , [ref] - [ref] , where all scalar and gauge field components live in $N×N$ color space.

Non-Abelian monopole-vortex complex · Remarks · 0.97
This moduli matrix formalism is very similar to the case of the $U(N)$ gauge theory with $N$ flavours of Higgs fields in the fundamental representation [ref] , except that here we have two gauge groups $SU(N), SU(N)$ besides a $U(1)$ gauge group.

Maximally Non-Abelian Vortices from Self-dual Yang--Mills Fields · Introduction · 0.96

Cites it as background 22 papers

The moduli space of multiple vortices at arbitrary positions with arbitrary orientations in the internal space was constructed in [ref] .

The Moduli Space Metric for Well-Separated Non-Abelian Vortices · Introduction · 0.89
Among the many remarkable developments which followed the discovery of genuine non-Abelian vortices (vortices with continuous non-Abelian moduli) in Refs. [ref] is the moduli matrix formalism [ref] (see review [ref] ), first constructed for domain walls.

Low-energy U(1) x USp(2M) gauge theory from simple high-energy gauge group · Introduction · 0.89
The most general Bogomol'nyi-Prasad-Sommerfield (BPS) vortex solutions and their moduli space have been found [ref] and the dynamics of two colliding vortices studied [ref] .

Constructing Non-Abelian Vortices with Arbitrary Gauge Groups · Introduction · 0.84

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