Periodic Supersymmetric Toda Lattice Hierarchy

Gribanov, V.V.; Kadyshevsky, V. G.; Сорин, А.С.

doi:10.1007/s10582-004-9791-1

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…In what follows we assume suitable boundary conditions for the functions f (m) k,j in order the main property of supertraces str[O, O} = 0 (10) be satisfied for the case of the generalized graded bracket (5).…”

Section: Space Of Difference Operatorsmentioning

confidence: 99%

Fermionic one- and two-dimensional Toda lattice hierarchies and their bi-Hamiltonian structures

2005

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By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N = (2|2) and N = (0|2) supersymmetric TL hierarchies as particular cases. Performing their reduction to the one-dimensional case by imposing suitable constraints we derive the corresponding 1D fermionic TL hierarchies. We develop the generalized graded R-matrix formalism using the generalized graded bracket on the space of graded operators with an involution generalizing the graded commutator in superalgebras, which allows one to describe these hierarchies in the framework of the Hamiltonian formalism and construct their first two Hamiltonian structures. The first Hamiltonian structure is obtained for both bosonic and fermionic Lax operators while the second Hamiltonian structure is established for bosonic Lax operators only. We propose the graded modified Yang-Baxter equation in the operator form and demonstrate that for the class of graded antisymmetric R-matrices it is equivalent to the tensor form of the graded classical Yang-Baxter equation.

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Section: Space Of Difference Operatorsmentioning

confidence: 99%

Fermionic one- and two-dimensional Toda lattice hierarchies and their bi-Hamiltonian structures

2005

Self Cite

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“…where the R-matrix is a linear map R: g → g such that the bracket (19) satisfies the properties (8-10). One can verify that the Jacobi identities (10) for the bracket (19) can equivalently be rewritten in terms of the generalized graded bracket (7)…”

Section: R-matrix Formalismmentioning

confidence: 99%

Hamiltonian Structures of Fermionic Two-Dimensional Toda Lattice Hierarchies

2006

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By exhibiting the corresponding Lax-pair representations, we propose a wide class of integrable twodimensional (2D) fermionic Toda lattice (TL) hierarchies, which includes the 2D N =(2|2) and N =(0|2) supersymmetric TL hierarchies as particular cases. We develop the generalized graded R-matrix formalism using the generalized graded bracket on the space of graded operators with involution generalizing the graded commutator in superalgebras, which allows describing these hierarchies in the framework of the Hamiltonian formalism and constructing their first two Hamiltonian structures. We obtain the first Hamiltonian structure for both bosonic and fermionic Lax operators and the second Hamiltonian structure only for bosonic Lax operators.

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“…Пять лет назад в работе [1], посвященной 75-летию академика Анатолия Алексеевича Логунова, мы рассмотрели квазиклассический предел суперсимметричной решеточной иерархии Тоды. За прошедшие годы мы неоднократно возвращались к этому кругу идей [2]- [4] и нашли неожиданные применения их в ряде разделов современной теоретической и математической физики. Выяснилось, в частности, что квазиклассический (бездисперсионный) предел решеточной иерархии Тоды связан с интегрируемой структурой, лежащей в основе полевой теории открытых (супер)струн на плоском геометрическом фоне [3], [4].…”

Section: посвящается 80-летию академика анатолия алексеевича логуноваunclassified

К Вопросу Об Интегрируемой Структуре Полевой Теории Открытых Суперструн

Кадышевский¹,

Sorin²

2006

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Найдены асимптотические разложения по "струнной массе" µ для µ-деформированных Γ-функций и коэффициентов Неймана, характеризующих трехструнную вершину в калибровке светового конуса полевой теории открытых суперструн на максимально суперсимметричном pp-волновом фоне. Ключевые слова: полевая теория струн, пространство анти-де Ситтера, иерархия Тоды.

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Periodic Supersymmetric Toda Lattice Hierarchy

Cited by 4 publications

References 13 publications

Fermionic one- and two-dimensional Toda lattice hierarchies and their bi-Hamiltonian structures

Fermionic one- and two-dimensional Toda lattice hierarchies and their bi-Hamiltonian structures

Hamiltonian Structures of Fermionic Two-Dimensional Toda Lattice Hierarchies

К Вопросу Об Интегрируемой Структуре Полевой Теории Открытых Суперструн

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