A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities

Jafarzade, Shahriyar; Nazari, Zainab

doi:10.48550/arxiv.1709.00070

Cited by 7 publications

(14 citation statements)

References 56 publications

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“…Comparison of Eqs. ( 6) and ( 7) with ( 8) and (9), respectively, provides a deep connection between supersymmetric quiver gauge theories and statistical mechanical theories, and this is an important point of the gauge/YBE correspondence. Until now the description has made manifest the correspondence between quiver diagram and statistical lattice, supersymmetric quiver gauge partition function and statistical partition function, vector multiplet in the adjoint representation and self-interaction term, chiral multiplet in the bifundamental representation and nearest-neighbour interaction, and holonomies of gauge fields and spin variables; but the relation between these sets of theories is actually deeper.…”

Section: Construction Of the Correspondencementioning

confidence: 98%

“…In Ref. [9] an integrable model is derived from Seiberg-like duality of 2d N = (2, 2) supersymmetric quiver gauge theories on T 2 . This model is shown to be a dimensional reduction of 4d N = 1 supersymmetric quiver gauge theories on T 2 × S 2 [30].…”

Section: From Seiberg-like Duality To Star-star Relationmentioning

confidence: 99%

“…Moreover, the contribution due to chiral and vector multiplets is given in terms of Jacobi theta functions, θ(y; q). The index duality of these 2d N = (2, 2) theories is given as follows [9] 1 2…”

Section: From Seiberg-like Duality To Star-star Relationmentioning

confidence: 99%

“…This have been done for different dimensions, amounts of supersymmetry, gauge groups and diverse curved manifolds. To state some examples, there are integrable models associated to 2d N = (2, 2) theories (see, for instance, [8,9]), 3d N = 2 theories (see, for instance, [10,11]) and 4d N = 1 theories (see, for instance, [12,13]). A large list of more dualities is given in [14].…”

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

2020

Preprint

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Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in 2d N = (0, 2) U Sp(2N ) supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in 2d N = (0, 2) U Sp(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 N = (0, 2) U Sp(2N ) theories with matter in the antisymmetric tensor representation that arises from dimensional reduction of 4d N = 1 U Sp(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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Section: Construction Of the Correspondencementioning

confidence: 98%

Section: From Seiberg-like Duality To Star-star Relationmentioning

confidence: 99%

Section: From Seiberg-like Duality To Star-star Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

de-la-Cruz-Moreno,

García-Compeán

2020

Preprint

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“…This interplay between supersymmetric theories and integrable models enable us to generate new solutions to the star-triangle relation which is a special form of the Yang-Baxter equation 1 , see e.g. [3][4][5][6][7][8][9]. The star-triangle relation is a sufficient condition for integrability of Ising-type lattice models [10,11].…”

mentioning

confidence: 99%

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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A slow review of the AGT correspondence

Floch¹

2022

J. Phys. A: Math. Theor.

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Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School ‘YRISW 2020’ to appear in a special issue of J. Phys. A. Class S is a wide class of 4d N = 2 supersymmetric gauge theories (ranging from super-QCD (quantum chromodynamics) to non-Lagrangian theories) obtained by twisted compactification of 6d N = ( 2 , 0 ) superconformal theories on a Riemann surface C. This 6d construction yields the Coulomb branch and Seiberg–Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d conformal field theory (CFT) correlators. For instance, the four-sphere partition function of a 4d N = 2 S U ( 2 ) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres–Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as T N correspond to Toda CFT correlators, and nonlocal operators (Wilson–’t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

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A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities

Cited by 7 publications

References 56 publications

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

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

Lens partition function, pentagon identity and star-triangle relation

A slow review of the AGT correspondence

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