On generalized Melvin solutions for Lie algebras of rank 3

Generalized Melvin solutions for rank-3 Lie algebras A3, B3 and C3 are considered. Any solution contains metric, three Abelian 2-forms and three scalar fields. It is governed by three moduli functions H1(z),H2(z),H3(z) (z = ρ2 and ρ is a radial variable), obeying three differential equations with certain boundary conditions imposed. These functions are polynomials with powers (n1,n2,n3) = (3, 4, 3), (6, 10, 6), (5, 8, 9) for Lie algebras A3, B3, C3, respectively. The solutions depend upon integration constants q1,q2,q3 ≠ 0. The power-law asymptotic relations for polynomials at large z are governed by integer-valued 3 × 3 matrix ν, which coincides with twice the inverse Cartan matrix 2A-1 for Lie algebras B3 and C3, while in the A3-case ν = A-1(I + P), where I is the identity matrix and P is a permutation matrix, corresponding to a generator of the ℤ2-group of symmetry of the Dynkin diagram. The duality identities for polynomials and asymptotic relations for solutions at large distances are obtained. Two-form flux integrals over a two-dimensional disc of radius R and corresponding Wilson loop factors over a circle of radius R are presented. © 2018 World Scientific Publishing Company.

Авторы
Редакторы
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Издательство
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Номер выпуска
7
Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
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Номер
1850108
Том
15
Год
2018
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 St., Moscow, 119361, Russian Federation
Ключевые слова
fluxbrane polynomials; Lie algebras; Melvin solution
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6552/