Matrix model from N = 2 orbifold partition function

Taro Kimura

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Matrix model from N = 2 orbifold partition function

Taro Kimura

High Energy Physics - Theory · Submitted 30 May 2011

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

The authors' main claim It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.

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The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function plays a crucial role on the orbifold projection. Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior. It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective.	contribution 0.67	0.75	0.07	asserted 0.68
s1	It is shown that the root of unity limit of the q-deformed partition function plays a crucial role on the orbifold projection.	result 0.98	0.86	0.16	asserted 1.00
s2	Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior.	contribution 0.56	0.94	0.31	asserted 1.00
s3	It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.	result 1.00	0.89	0.38	asserted 1.00

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Original abstract

The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function plays a crucial role on the orbifold projection. Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior. It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.

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References

Forward citations

Cited by 2 Pith papers

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

4d Index to 3d Index and 2d TQFT
hep-th 2011-09 conditional novelty 6.0 of 10

The 4d superconformal index on S^1 x L(p,1) is computed exactly and shown to reduce to a 3d index as p grows and to a 3d lens-space partition function as the time circle shrinks.
Instantons on ALE spaces and Super Liouville Conformal Field Theories
hep-th 2011-06 conditional novelty 6.0 of 10

The SU(2) Nekrasov partition function on the resolved C^2/Z_2 ALE space reproduces N=1 super Liouville conformal blocks, with the Ramond sector matching half-integer first Chern class sectors.

How the literature uses it

17 arXiv papers cite this in 41 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 · 20 sentences without a confident label

Builds on it 1 paper

In this paper we develop the previous result [ref] , and consider a systematic method to deal with the combinatorial representation of the partition function for the generic four dimensional toric orbifolds $^2/Γ_r,s$, whose boundary is the generic lens space $L(r,s)$.

Beta-ensembles for toric orbifold partition function · Introduction · 1.00

Uses its method or tool 2 papers

According to the method developed in [ref] , the prescription to extract the $Γ$-invariant state is as follows: (i) lifting it up to the $q$-deformed state, and then (ii) taking a non-standard limit, i.e. the root of unity limit of such a $q$-deformed theory, $q →ω_M$.

Spinless basis for spin-singlet FQH states · From Laughlin to Halperin · 1.00
In this case we introduce a slightly different way of decomposition [ref] , [equation] where $c_i^(l,v)$ stands for the mapping from the index of the divided $nr$-partition to that of the original $n$-partition.

Beta-ensembles for toric orbifold partition function · Instanton counting on toric orbifolds · 0.86

Compares with it 1 paper

Thus the second part in ([ref]) leads to the matrix potential, [equation] [equation] This potential function is completely the same as the previous result [ref] .

Beta-ensembles for toric orbifold partition function · Matrix model description · 1.00

Cites it as background 9 papers

[ The Uglov matrix model is originally introduced to describe the $ℤ_r$ orbifold theory [ref] .

Virasoro Constraint for Uglov Matrix Model · Ward identity · 0.92
0 Hanany-Tong [ref] moduli space [ref] higher winding numbers [ref] group theory [ref] vortex counting [ref] [ref] instantons on the ALE spaces [ref] collision [ref] moduli space metric [ref] review: HT $↔$ moduli matrix [ref] instanton counting on the ALE spaces [ref] AGT for the ALE spaces [ref] vortex polygon and crystal [ref]

Vortices on Orbifolds · Introduction · 0.99
The role of the root of unity limit in the context of gauge theory is discussed in [ref] .] We denote the inverse of the $q$-Cartan matrix by $𝐜̃$.

Double Quiver Gauge Theory and BPS/CFT Correspondence · Orbifold instanton partition function · 0.95

What it cites · 51 sentences without a confident label

Builds on 4 papers

This relation is extended to the theory with the generalized $W$ algebra [ref] [ref] [ref] , which is obtained from the quantum Drinfeld-Sokolov reduction applied to an affine Lie algebra $(n)$ [ref] .

Affine SL(2) conformal blocks from 4d gauge theories · String theory perspective · 0.95
This relation is extended to the theory with the generalized $W$ algebra [ref] [ref] [ref] , which is obtained from the quantum Drinfeld-Sokolov reduction applied to an affine Lie algebra $(n)$ [ref] .

Affine sl(N) conformal blocks from N=2 SU(N) gauge theories · String theory perspective · 0.95
This relation is extended to the theory with the generalized $W$ algebra [ref] [ref] [ref] , which is obtained from the quantum Drinfeld-Sokolov reduction applied to an affine Lie algebra $(n)$ [ref] .

On W-algebras and the symmetries of defects of 6d N=(2,0) theory · String theory perspective · 0.95

Uses the method or tool of 4 papers

By decomposing the partition functions ([ref]), ([ref]) as [equation] each part can be rewritten as [equation] We can check finite constants turn out to be [equation] Therefore they can be represented as [equation] [equation] These expressions are convenient to give the matrix model description [ref] .

Seiberg-Witten theory and matrix models · $=2$ partition functions · 0.85
By decomposing the partition functions ([ref]), ([ref]) as [equation] each part can be rewritten as [equation] We can check finite constants turn out to be [equation] Therefore they can be represented as [equation] [equation] These expressions are convenient to give the matrix model description [ref] .

Matrix models for 2* theories · $=2$ partition functions · 0.85
By decomposing the partition functions ([ref]), ([ref]) as [equation] each part can be rewritten as [equation] We can check finite constants turn out to be [equation] Therefore they can be represented as [equation] [equation] These expressions are convenient to give the matrix model description [ref] .

Matrix models for $\beta$-ensembles from Nekrasov partition functions · $=2$ partition functions · 0.85

Compares with 13 papers

This matrix model, which we now call $q$-Virasoro matrix model, is apparently different from the trigonometric one [ref] , but it is worth considering the root of unity limit of such a $q$-Virasoro related models.

Matrix models for 2* theories · $q$-deformed CFT · 0.93
This matrix model, which we now call $q$-Virasoro matrix model, is apparently different from the trigonometric one [ref] , but it is worth considering the root of unity limit of such a $q$-Virasoro related models.

Matrix models for $\beta$-ensembles from Nekrasov partition functions · $q$-deformed CFT · 0.93
This matrix model, which we now call $q$-Virasoro matrix model, is apparently different from the trigonometric one [ref] , but it is worth considering the root of unity limit of such a $q$-Virasoro related models.

Seiberg-Witten theory and matrix models · $q$-deformed CFT · 0.93

Cites as background 19 papers

Furthermore another type of the matrix model is also investigated so far [ref] [ref] .

Matrix models for $\beta$-ensembles from Nekrasov partition functions · Introduction · 0.90
Furthermore another type of the matrix model is also investigated so far [ref] [ref] .

Seiberg-Witten theory and matrix models · Introduction · 0.90
Furthermore another type of the matrix model is also investigated so far [ref] [ref] .

Instanton Counting and Matrix Model · Introduction · 0.90

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