4d $\mathcal{N}=1$ quiver gauge theories and the $\mathrm{A_n}$ Bailey lemma

Frederic Br\"unner; Vyacheslav P. Spiridonov

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4d $\mathcal{N}=1$ quiver gauge theories and the $\mathrm{A_n}$ Bailey lemma

Frederic Brünner, Vyacheslav P. Spiridonov

High Energy Physics - Theory · Submitted 19 Dec 2017

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

The authors' main claim Interpreting integrals as superconformal indices of four-dimensional $\mathcal{N}=1$ quiver gauge theories with the gauge groups being copies of $\mathrm{SU(n+1)}$, we provide evidence for various new dualities.

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arXiv ID1712.07018 (version 1)

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CitationFrederic Br\"unner, Vyacheslav P. Spiridonov. "4d $\mathcal{N}=1$ quiver gauge theories and the $\mathrm{A_n}$ Bailey lemma." arXiv:1712.07018 (2017). https://pith.science/paper/F4HSPVIC

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We study the integral Bailey lemma associated with the $\mathrm{A_n}$-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional $\mathcal{N}=1$ quiver gauge theories with the gauge groups being copies of $\mathrm{SU(n+1)}$, we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the integral Bailey lemma associated with the $\mathrm{A_n}$-root system and identities for elliptic hypergeometric integrals generated thereby.	contribution 1.00	0.88	0.10	asserted 0.85
s1	Interpreting integrals as superconformal indices of four-dimensional $\mathcal{N}=1$ quiver gauge theories with the gauge groups being copies of $\mathrm{SU(n+1)}$, we provide evidence for various new dualities.	contribution 0.37	0.93	0.43	hedged possibility 0.69
s2	Further confirmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds.	result 0.47	0.89	0.11	asserted 0.98
s3	We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.	contribution 0.69	0.88	0.21	hedged possibility 0.96

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Original abstract

We study the integral Bailey lemma associated with the $\mathrm{A_n}$-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional $\mathcal{N}=1$ quiver gauge theories with the gauge groups being copies of $\mathrm{SU(n+1)}$, we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

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7 arXiv papers cite this in 8 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show that applying the Bailey lemma to elliptic hypergeometric integrals on the $A_n$ root system leads to a large web of dualities for $\mathcal{N} = 1$ supersymmetric linear quiver theories.

A duality web of linear quivers · 0.82

Papers citing it · 6 sentences without a confident label

Cites it as background 2 papers

Recently, several Bailey pairs were constructed via supersymmetric gauge theory computations, and integrable lattice spin models of statistical mechanics [ref] .

A remark on the q-hypergeometric integral Bailey pair and the solution to the star-triangle equation · Introduction · 0.84
In recent years, the remarkable concept of hypergeometric identities sits at the intersection of diverse studies such as exact results in supersymmetric gauge theories [ref] and their mathematical structures interacting with various fields in mathematics, see, e.g., [ref] , star-triangle relation (Yang-Baxter equation) [ref] or star-star relation [ref] for spin lattice models, knot theory [ref] , pentagon identities [ref] , Bailey pairs [ref] , quantum algebras [ref] , etc.

On Bailey pairs for $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$ · Introduction · 1.00

What it cites · 6 sentences without a confident label

Cites as background 2 papers

Many interesting results have since been derived on the theory of these objects; see [ref] for an exposition to the subject.

Essays on the theory of elliptic hypergeometric functions · Introduction · 1.00
Elliptic hypergeometric integrals related to the latter were studied in [ref] .

Rarefied elliptic hypergeometric functions · Conclusion · 0.87

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