Integrable deformations of CFTs and the discrete Hirota equations

Nahm, W.; Keegan, Sinéad

doi:10.48550/arxiv.0905.3776

Cited by 8 publications

(13 citation statements)

References 10 publications

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“…Q-systems, which arise from the Bethe ansatz for quantum integrable models, provide further examples of nonlinear recurrences which are obtained from sequences of cluster mutations [14], and are also linearisable in the above sense [2]. They correspond to characters of representations of Yangian algebras, as well as being reductions of discrete Hirota equations [17]. The simplest case is the A 1 Q-system, which coincides with (1.2).…”

Section: Introductionmentioning

confidence: 99%

A family of linearizable recurrences with the Laurent property

Hone

Ward

2014

Bulletin of the London Mathematical Society

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We consider a family of non-linear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced recently by Lam and Pylyavskyy. Furthermore, each member of this family is shown to be linearizable in two different ways, in the sense that its iterates satisfy both a linear relation with constant coefficients and a linear relation with periodic coefficients. Associated monodromy matrices and first integrals are constructed, and the connection with the dressing chain for Schrödinger operators is also explained.

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Section: Introductionmentioning

confidence: 99%

A family of linearizable recurrences with the Laurent property

Hone

Ward

2014

Bulletin of the London Mathematical Society

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“…Here for i, j ∈ {1, 2, 3}, [T (x i )T (x j )] reg. is defined by (16). By part 2 in the Proof of Theorem 2, [T (x i )T (x j )] reg.…”

Section: Graph Representation Of the Virasoro N-point Functionmentioning

confidence: 99%

“…The case of the Riemann sphere X 0 is easy, and for the torus X 1 , one can use the standard tools of doubly periodic and modular functions ( [23], [2] and more recently, e.g. [3], [16]). The case g > 1 is technically more demanding, however.…”

Section: Introductionmentioning

confidence: 99%

Virasoro Correlation Functions on Hyperelliptic Riemann Surfaces

Leitner

2013

Lett Math Phys

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N -point functions of holomorphic fields in conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulas for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus g ≥ 1. Virasoro N -point functions for higher N are obtained inductively, and we show that they have a nice graph representation. We discuss the 3-point function with application to the (2, 5) minimal model.

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“…Example 5.8. In type G 2 , we have t 1 = 1, t 2 = 3, e 1 = 6, e 2 = 10, h ∨ = 4, c 1 = 3, c 2 = 21, h 1 = (1, 8, 8, 1) and h 2 = (1,7,34,122,344,803,1581,2683,3952,5100,5785,5785,5100,3952,2683,1581,803,344,122,34,7,1).…”

Section: Dimensions Of Kirillov-reshetikhin Modules In Exceptional Typesmentioning

confidence: 99%

“…For example, those relations in type A are considered in [11] from the viewpoint of integrable systems. They are also studied in [34] for type A and D, motivated from a problem in number theory. In [5] a gauge theoretic discussion on the topic appeared.…”

Section: Introductionmentioning

confidence: 99%

Linear Recurrence Relations in Q-Systems via Lattice Points in Polyhedra

Lee

2018

Transformation Groups

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We prove that the sequence of the characters of the Kirillov-Reshetikhin (KR) modules W (a) m , m ∈ Z m≥0 associated to a node a of the Dynkin diagram of a complex simple Lie algebra g satisfies a linear recurrence relation except for some cases in types E 7 and E 8 . To this end we use the Q-system and the existing lattice point summation formula for the decomposition of KR modules, known as domino removal rules when g is of classical type. As an application, we show how to reduce some unproven lattice point summation formulas in exceptional types to finite problems in linear algebra and also give a new proof of them in type G 2 , which is the only completely proven case when KR modules have an irreducible summand with multiplicity greater than 1. We also apply the recurrence to prove that the function dim W (a) m is a quasipolynomial in m and establish its properties. We conjecture that there exists a rational polytope such that its Ehrhart quasipolynomial in m is dim W (a) m and the lattice points of its m-th dilate carry the same crystal structure as the crystal associated with W (a) m .

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Integrable deformations of CFTs and the discrete Hirota equations

Cited by 8 publications

References 10 publications

A family of linearizable recurrences with the Laurent property

A family of linearizable recurrences with the Laurent property

Virasoro Correlation Functions on Hyperelliptic Riemann Surfaces

Linear Recurrence Relations in Q-Systems via Lattice Points in Polyhedra

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