Vortex counting from field theory

Keisuke Ohashi; Muneto Nitta; Taro Kimura; Toshiaki Fujimori

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Vortex counting from field theory

Toshiaki Fujimori, Taro Kimura, Muneto Nitta, Keisuke Ohashi

High Energy Physics - Theory · Submitted 9 Apr 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets.

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The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach. The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula. We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets. The orbifold vortex partition function is also investigated from the field theoretical point of view.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach.	contribution 0.82	0.90	0.26	asserted 1.00
s1	The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula.	method 0.99	0.86	0.16	asserted 1.00
s2	We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets.	result 0.92	0.95	0.32	asserted 1.00
s3	The orbifold vortex partition function is also investigated from the field theoretical point of view.	contribution 1.00	0.84	0.06	asserted 0.99

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The paper

Original abstract

The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach. The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula. We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets. The orbifold vortex partition function is also investigated from the field theoretical point of view.

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References

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Exact Results in D=2 Supersymmetric Gauge Theories
hep-th 2012-06 accept novelty 8.0 of 10

The S^2 partition function of 2d N=(2,2) gauge theories equals both a Coulomb-branch integral and a Higgs-branch vortex sum, and for SQED it equals a Toda CFT correlator.
Fractional Superfluid Vortices and Worldsheet Wess--Zumino--Witten Models in Two-Color QCD and $Sp(2N)$ Gauge Theories
hep-th 2026-09 conditional novelty 7.0 of 10

Minimal superfluid vortices in even-flavor pseudoreal gauge theories wind only 1/m of the baryon circulation quantum and localize Sp(2m)_N WZW conformal field theories with central charge Nm(2m+1)/(N+m+1).
Opers, surface defects, and Yang-Yang functional
hep-th 2018-06 conditional novelty 7.0 of 10

The effective twisted superpotential of Ω-deformed N=2 quiver gauge theories equals the generating function of the variety of opers in generalized NRS Darboux coordinates, proven for SL(2) and SL(3).
Partition functions of N=(2,2) gauge theories on S^2 and vortices
hep-th 2012-06 accept novelty 7.0 of 10

Localizing two-dimensional N=(2,2) gauge theories on S^2 yields a matrix integral that equals a sum of vortex-times-antivortex partition functions, and this equality proves the Hori-Tong duality at the level of partit...
Higgs branch localization of 3d N=2 theories
hep-th 2013-12 conditional novelty 6.0 of 10

Higgs branch localization directly produces the vortex-times-anti-vortex factorization of 3d N=2 partition functions on the squashed sphere and S^1 x S^2, extending it to more general matter content.

Show 1 more citing papers

Vertices, Vortices & Interacting Surface Operators
hep-th 2011-02 conditional novelty 6.0 of 10

The vortex partition function of N=(2,2) gauge theories with adjoint and anti-fundamental matter equals the field-theory limit of the topological vertex on a strip with column-diagram boundary conditions, and resums i...

How the literature uses it

15 arXiv papers cite this in 21 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 · 14 sentences without a confident label

Uses its method or tool 1 paper

Taking $t →∞$, the saddle points for bosonic fields are given by zeros of supersymmetric variation ([ref]), ([ref]) and ([ref]) as [equation] If we take the gauge fixing condition as $∂_t A_ω̅=0$, then ([ref]) reduces to the constant matrix valued equations, namely [equation] These equations are the fixed points equation for the vortex moduli space under the equivariant rotation with respect to $U(1)^N_f-1_m ×U(1)_ε$ [ref] .

Higgs branch localization of 3d N=2 theories · Vortex partition function of 3d $𝒩=2$ theory with fundamental and anti-fundamental chiral multiplets · 0.82

Compares with it 1 paper

The vortex partition function ([ref]) also agrees with [ref] for $N_f = N$, apart from a possible minus sign in front of $z$ which can be reabsorbed by a redefinition of the theta angle.

Partition functions of N=(2,2) gauge theories on S^2 and vortices · $U(N)$ with $(N_f,N_a)$ flavors · 1.00

Cites it as support 1 paper

This reflects a fact that anti-fundamental and adjoint scalars can contribute only to the Fermionic moduli [ref] .

Higgs branch localization of 3d N=2 theories · At north and south poles · 0.98

Cites it as background 3 papers

This situation is extensively considered in the literature, but the ADHM-like analysis is not so clear except for the simpler (Abelian) configurations (e.g. $r_A∈{0,1}$ in our notation, we refer to [ref] for recent discussions), especially in view of the pure vortex analysis in [ref] .

Intersecting Defects and Supergroup Gauge Theory · Comments and open questions · 0.91
See also [ref] for a very recent work.

Vortices and 3 dimensional dualities · Introduction · 0.93
[ [ref] ] T.~Fujimori, T.~Kimura, M.~Nitta, and K.~Ohashi,\\ Vortex counting from field theory,\\ https://doi.org/10.1007/JHEP06(2012)028JHEP 1206 (2012), 028, https://arxiv.org/abs/1204.1968 arXiv:1204.1968 [hep-th].\\[-.5em]

Instanton Counting, Quantum Geometry and Algebra · Introduction · 0.90

What it cites · 42 sentences without a confident label

Contests 2 papers

On the other hand, it is shown that, although Hanany-Tong's approach can capture the global structure of the vortex moduli space, the local structure is not correctly treated: the metric of the moduli space is different from the result obtained from the purely field theoretical method [ref] .

The Moduli Space Metric for Well-Separated Non-Abelian Vortices · Introduction · contest 0.78
On the other hand, it is shown that, although Hanany-Tong's approach can capture the global structure of the vortex moduli space, the local structure is not correctly treated: the metric of the moduli space is different from the result obtained from the purely field theoretical method [ref] .

Vortices, Instantons and Branes · Introduction · contest 0.78

Builds on 1 paper

These conditions are regarded as natural extensions of the original one, which is discussed in [ref] .

Vortices on Orbifolds · Summary and discussion · 0.91

Uses the method or tool of 9 papers

In this paper we apply the moduli matrix approach to study the vortex moduli space [ref] .

Universal Reconnection of Non-Abelian Cosmic Strings · Introduction · 1.00
In this paper we apply the moduli matrix approach to study the vortex moduli space [ref] .

The Moduli Space Metric for Well-Separated Non-Abelian Vortices · Introduction · 1.00
In this paper we apply the moduli matrix approach to study the vortex moduli space [ref] .

Dynamics of Non-Abelian Vortices · Introduction · 1.00

Compares with 3 papers

This character correctly reproduces the previous result [ref] .

The Liouville side of the Vortex · Adding anti-fundamental matters · 0.96
This character correctly reproduces the previous result [ref] .

On F-term contribution to effective action · Adding anti-fundamental matters · 0.96
This character correctly reproduces the previous result [ref] .

Vertices, Vortices & Interacting Surface Operators · Adding anti-fundamental matters · 0.96

Cites as background 39 papers

Recently partition functions have been provided for the low dimensional gauge theories by performing vortex counting [ref] , where non-Abelian vortices in $(N)$ gauge theories [ref] play roles of instantons in two dimensions.

Vortices, Instantons and Branes · Introduction · 0.93
Recently partition functions have been provided for the low dimensional gauge theories by performing vortex counting [ref] , where non-Abelian vortices in $(N)$ gauge theories [ref] play roles of instantons in two dimensions.

Quantum Vortex Strings: A Review · Introduction · 0.93
Recently partition functions have been provided for the low dimensional gauge theories by performing vortex counting [ref] , where non-Abelian vortices in $(N)$ gauge theories [ref] play roles of instantons in two dimensions.

Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories · Introduction · 0.93

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