Integrability as duality: The Gauge/YBE correspondence

Yamazaki, Masahito

doi:10.1016/j.physrep.2020.01.006

Cited by 13 publications

(21 citation statements)

References 105 publications

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“…In another direction, the lens elliptic gamma function, which is a central function for this paper, first appeared in the study of four-dimensional N = 1 supersymmetric gauge theories on a circle times the lens space S 3 /Z r [7]. This connection suggests that there exists an interpretation of the results of this paper in terms of supersymmetric gauge theories and associated integrable lattice models [8,[11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 71%

Lens Generalisation of τ-Functions for the Elliptic Discrete Painlevé Equation

Kels

Yamazaki

2019

International Mathematics Research Notices

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We propose a new bilinear Hirota equation for τ-functions associated with the E 8 root lattice, that provides a "lens" generalisation of the τ-functions for the elliptic discrete Painlevé equation. Our equations are characterized by a positive integer r in addition to the usual elliptic parameters, and involve a mixture of continuous variables with additional discrete variables, the latter taking values on the E 8 root lattice. We construct explicit W(E 7 )-invariant hypergeometric solutions of this bilinear Hirota equation, which are given in terms of elliptic hypergeometric sum/integrals. 14 5.2. Decomposition of τ-function 16 6. Hypergeometric τ-Function 18 6.

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Section: Introductionmentioning

confidence: 71%

Lens Generalisation of τ-Functions for the Elliptic Discrete Painlevé Equation

Kels

Yamazaki

2019

International Mathematics Research Notices

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“…There are plenty of integrable models that have been obtained from supersymmetric dualities via the gauge/YBE correspondence [7]. This have been done for different dimensions, amounts of supersymmetry, gauge groups and diverse curved manifolds.…”

Section: Jhep01(2021)023mentioning

confidence: 99%

“…As stated in [7], an integrable model is considered to be a solution of the Yang-Baxter equation with spectral parameters that satisfies the rapidity difference property in their R-matrices…”

Section: Overview Of Gauge/ybe Correspondencementioning

confidence: 99%

“…The review of this subsection is carried out mainly following ref. [7]. For a quiver gauge theory in dimension d with gauge group G, let V and E be the sets of all vertices and edges in its associated quiver diagram, respectively.…”

Section: Construction Of the Correspondencementioning

confidence: 99%

“…Recently, a surprising relation between quiver gauge theories in various dimensions with diverse degrees of supersymmetry and integrable models in statistical mechanics has starting to be explored by many authors, for an overview see [7] and references therein. This relation is termed in the literature as the gauge/YBE correspondence.…”

Section: Introductionmentioning

confidence: 99%

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Star-triangle type relations from 2d $$ \mathcal{N} $$ = (0, 2) USp(2N) dualities

de-la-Cruz-Moreno

García‐Compeán

2021

J. High Energ. Phys.

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Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in 2d$$ \mathcal{N} $$ N = (0, 2) USp(2N) supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in 2d$$ \mathcal{N} $$ N = (0, 2) USp(2N) theories. The description is performed explicitly for N = 1, 2, 3, 4, 5 and also for N = 3k + 2, which generalizes the situation in N = 2, 5. For N = 1 a triangle identity is obtained. For N = 2, 5 it is found that the realization of duality implies slight variations of a star-triangle relation type (STR type). The values N = 3, 4 are associated to a similar version of the asymmetric STR. The second case is a new duality for 2d$$ \mathcal{N} $$ N = (0, 2) USp(2N) theories with matter in the antisymmetric tensor representation that arises from dimensional reduction of 4d$$ \mathcal{N} $$ N = 1 USp(2N) Csáki-Skiba-Schmaltz duality. It is shown that this duality is associated to a triangle type identity for any value of N. In all cases Boltzmann weights as well as interaction and normalization factors are completely determined. Finally, our relations are compared with those previously reported in the literature.

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On Bailey pairs for $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on $$ {S}_b^3/{\mathbb{Z}}_r $$

Gahramanov

Keskin

Dilara

et al. 2023

J. High Energ. Phys.

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We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories on $$ {S}_b^3/{\mathbb{Z}}_r $$ S b 3 / ℤ r . The novel Bailey pairs are constructed for the star-triangle relation, the star-star relation, and the pentagon identity. The first two of them are integrability conditions for the Ising-type integrable lattice models. The last one corresponds to the representation of the basic 2 − 3 Pachner move for triangulated 3-manifolds.

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Integrability as duality: The Gauge/YBE correspondence

Cited by 13 publications

References 105 publications

Lens Generalisation of τ-Functions for the Elliptic Discrete Painlevé Equation

Lens Generalisation of τ-Functions for the Elliptic Discrete Painlevé Equation

Star-triangle type relations from 2d $$ \mathcal{N} $$ = (0, 2) USp(2N) dualities

On Bailey pairs for $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on $$ {S}_b^3/{\mathbb{Z}}_r $$

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