New Pentagon Identities Revisited

Jafarzade, Shahriyar

doi:10.1088/1742-6596/1194/1/012054

Cited by 6 publications

(9 citation statements)

References 21 publications

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“…There are several pentagon identities in terms of Euler's gamma function [24,40,49]. Here we present the known pentagon relation [24] in terms of gamma function which we obtained in different manner 12 .…”

Section: Limit Of the Pentagon Identitymentioning

confidence: 78%

“…There are several examples of integral pentagon relations computed via three-dimensional supersymmetric dualities, see, e.g. [24,[40][41][42][43][45][46][47]. Here we present a new pentagon identity in terms of hyperbolic gamma functions.…”

Section: Pentagon Identitymentioning

confidence: 93%

“…The Euler's gamma function limit of the integral identity (1.1) gives the known solution to the startriangle relation [23], also can be written as the pentagon identity presented in [24]. From supersymmetric gauge theory side, by taking such a limit (r → ∞) one obtains the partition function of two-dimensional N = (2, 2) supersymmetric gauge theories on two-sphere S 2 .…”

mentioning

confidence: 99%

“…SUSY duality with G = U (1) on S 3 /Zr [26] SUSY duality with G = SU (2) on S 3 /Zr [9] Star-Triangle relation for Uq(osp(1|2)) [25] Star-Triangle Relation Pentagon identity Special case of Faddeev-Volkov [22] Pentagon identity [24] P P P P P P P P P P P P P…”

mentioning

confidence: 99%

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Lens partition function, pentagon identity and star-triangle relation

Bozkurt,

Gahramanov,

Mullahasanoglu

2020

Preprint

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We study the three-dimensional lens partition function for N = 2 supersymmetric gauge dual theories on S 3 /Z r by using the gauge/YBE correspondence. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the three-dimensional supersymmetric dual theories can be written as an integral identity for hyperbolic hypergeometric functions. We obtain such an integral identity which can be written as the star-triangle relation for Ising type integrable models and as the integral pentagon identity. The latter represents the basic 2-3 Pachner move for triangulated 3-manifolds. A special case of our integral identity can be used for proving orthogonality and completeness relation of the Clebsch-Gordan coefficients for the self-dual continuous series of U q (osp(1|2)).

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Section: Limit Of the Pentagon Identitymentioning

confidence: 78%

Section: Pentagon Identitymentioning

confidence: 93%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Lens partition function, pentagon identity and star-triangle relation

Bozkurt,

Gahramanov,

Mullahasanoglu

2020

Preprint

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“…Such identities also play a role in the study of supersymmetric gauge theories, integrable models, knot theory, etc. (see some recent works [3][4][5][6][7][8][9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

Bailey pairs for the q-hypergeometric integral pentagon identity

Gahramanov¹,

Erkan²

2021

Preprint

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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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New Pentagon Identities Revisited

Cited by 6 publications

References 21 publications

Lens partition function, pentagon identity and star-triangle relation

Lens partition function, pentagon identity and star-triangle relation

Bailey pairs for the q-hypergeometric integral pentagon identity

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

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