On generalized Melvin solutions for Lie algebras of rank 3

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model contains n 2-forms and l > n scalar fields, where n is the rank of G. The solution is governed by a set of n functions Hs (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials Hs (z), s = 1,..., 6, corresponding to the Lie algebra E 6 are obtained. They depend upon integration constants Qs, s = 1,..., 6 . The polynomials obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances which are presented in the paper. The power-law asymptotic relations for E 6-polynomials at large z are governed by integer-valued matrix v = A -1 (I + P), where A -1 is inverse Cartan matrix, I is identity matrix and P is permutation matrix, corresponding to a generator of the Z 2-group of symmetry of the Dynkin diagram. The 2-form fluxes Φs are calculated, s = 1, ..., 6. © Published under licence by IOP Publishing Ltd.

Авторы
Редакторы
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Сборник материалов конференции
Издательство
Institute of Physics Publishing
Номер выпуска
1
Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
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Ссылка
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Номер
012093
Том
1390
Год
2019
Организации
  • 1 Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, RUDN University, 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
  • 2 Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya ul., Moscow, 119361, Russian Federation
Ключевые слова
Astrophysics; Boundary conditions; High energy physics; Inverse problems; Ordinary differential equations; Polynomials; Gravitational model; Identity matrices; Integer-valued matrices; Integration constants; Multidimensional generalization; Permutation matrix; Scalar fields; Simple lie algebras; Matrix algebra
Дата создания
10.02.2020
Дата изменения
10.02.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/56312/