Fluxbrane Polynomials and Melvin-like Solutions for Simple Lie Algebras

This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and n scalar fields coupled to n Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank n. The set of n moduli functions Hs(z) comply with n non-linear (ordinary) differential equations (of second order) with certain boundary conditions set. Earlier, it was hypothesized that these moduli functions should be polynomials in z (so-called “fluxbrane” polynomials) depending upon certain parameters ps>0, s=1,…,n. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks n=1,2,3,4,5 and exceptional algebra E6. Certain relations for the polynomials (e.g., symmetry and duality ones) were outlined. In a general case where polynomial conjecture holds, 2-form flux integrals are finite. The use of fluxbrane polynomials to dilatonic black hole solutions was also explored.

Авторы
Журнал
Издательство
MDPI AG
Номер выпуска
6
Язык
Английский
Страницы
1199
Статус
Опубликовано
Том
15
Год
2023
Организации
  • 1 Institute of Gravitation and Cosmology, RUDN University, 6 Miklukho-Maklaya Str., 117198 Moscow, Russia
  • 2 Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Str., 119361 Moscow, Russia
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