Integrable Lattice Spin Models from Supersymmetric Dualities

Gahramanov, Ilmar; Jafarzade, Shahriyar

doi:10.1134/s1547477118060079

Cited by 25 publications

(24 citation statements)

References 131 publications

(209 reference statements)

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“…See[6,12,15] for the relation between supersymmetric dualities and star-triangle relation. More information about pentagon identities and star-triangle relations see[19].…”

mentioning

confidence: 99%

New Pentagon Identities Revisited

Jafarzade

2019

J. Phys.: Conf. Ser.

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We present a new solution to the pentagon identity in terms of gamma function. We obtain this solution by taking the gamma function limit from the pentagon identity related to the three-dimesional index. This limit corresponds to the identification of the sphere partition function of dual theories and being equivalent to the star-triangle relation in statistical mechanics which corresponds to the "strongly coupled" regime of the Faddeev-Volkov model.

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“…See[6,12,15] for the relation between supersymmetric dualities and star-triangle relation. More information about pentagon identities and star-triangle relations see[19].…”

mentioning

confidence: 99%

New Pentagon Identities Revisited

Jafarzade

2019

J. Phys.: Conf. Ser.

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“…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]. Despite the rich zoo of new integrable models obtained from the gauge/YBE correspondence and as far as we know, there are no explicit integrable models associated with 2d N = (0, 2) theories and we have found very few literature about this topic (see, for example, [15] for the context of brane constructions).…”

Section: Jhep01(2021)023mentioning

confidence: 99%

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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“…10 The double sine function is a variant of Faddeev's non-compact quantum dilogarithm [19]. There are different notations and modifications of this function, relations between some of them can be found in [6,37,38]. 11 This identity first was proven for the case m = 0 [32].…”

Section: Pentagon Identitiesmentioning

confidence: 99%

Pentagon Identities Arising in Supersymmetric Gauge Theory Computations

Bozkurt

Gahramanov

2019

Theor Math Phys

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The partition functions of three-dimensional N = 2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. By comparing the partition functions of three-dimensional mirror dual theories, one finds complicated integral identities. In some cases, these identities can be written in the form of pentagon relations. Such identities often have an interpretation as the Pachner's 3-2 move for triangulated manifolds via the so-called 3d-3d correspondence. From the physics perspective, another important application of pentagon identities is that they may be used to construct new solutions to the quantum Yang-Baxter equation.

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Integrable Lattice Spin Models from Supersymmetric Dualities

Cited by 25 publications

References 131 publications

New Pentagon Identities Revisited

New Pentagon Identities Revisited

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

Pentagon Identities Arising in Supersymmetric Gauge Theory Computations

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