A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations

Bazhanov, Vladimir V.; Сергеев, С. М.

doi:10.48550/arxiv.1006.0651

Cited by 18 publications

(59 citation statements)

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“…In the present paper we concentrated mostly on the spin-zero case, while the elaboration of the spin non-zero case is the subject of a future publication, some initial results of which were already presented in [22]. As a direction for the future, establishing connections, if any, with the recently found master-solutions of the quantum Yang-Baxter equations, [6], may be of interest.…”

Section: Discussionmentioning

confidence: 99%

On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants

Delice¹,

Nijhoff²,

Yoo-Kong³

2014

J. Phys. A: Math. Theor.

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A general elliptic N × N matrix Lax scheme is presented, leading to two classes of elliptic lattice systems, one which we interpret as the higher-rank analogue of the Landau-Lifschitz equations, while the other class we characterize as the higher-rank analogue of the lattice Krichever-Novikov equation (or Adler's lattice). We present the general scheme, but focus mainly of the latter type of models. In the case N = 2 we obtain a novel Lax representation of Adler's elliptic lattice equation in its so-called 3-leg form. The case of rank N = 3 is analysed using Cayley's hyperdeterminant of format 2 × 2 × 2, yielding a multi-component system of coupled 3-leg quad-equations.

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Section: Discussionmentioning

confidence: 99%

On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants

Delice¹,

Nijhoff²,

Yoo-Kong³

2014

J. Phys. A: Math. Theor.

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“…For the proof see[22], also see[24] for a check via series expansion 8. Interestingly, this integral identity arises in different fields of theoretical physics, particularly, it is a startriangle relation of an integrable lattice model[42,43]. Also note that limits of the beta integral lead to many identities for hypergeometric integrals, for instance, the limit p → 0 gives the Nassrallah-Rahman integral[44].…”

mentioning

confidence: 95%

A new pentagon identity for the tetrahedron index

Gahramanov

Rosengren

2013

J. High Energ. Phys.

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Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional N = 2 supersymmetric theories and give a mathematical proof of it.

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“…Around 2010, it was discovered that supersymmetric indices of certain fourdimensional N = 1 supersymmetric gauge theories coincide with the partition functions of two-dimensional integrable lattice models in statistical mechanics. [1][2][3] As was later recognized, 4 these gauge theories are realized by particular configurations of branes in string theory, called brane tilings. 5,6 The lattice models in question are known as the Bazhanov-Sergeev models 1,3 and have continuous spin variables.…”

Section: Introductionmentioning

confidence: 94%