https://doi.org/10.1140/epjc/s10052-017-5235-5
Regular Article - Theoretical Physics
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
1
Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Str., Moscow, 119361, Russia
2
Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow, 117198, Russia
* e-mail: ivashchuk@mail.ru
Received:
27
June
2017
Accepted:
12
September
2017
Published online:
30
September
2017
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra 
is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of . It is governed by a set of n moduli functions 
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. These polynomials depend upon integration constants 
, 
. In the case when the conjecture on the polynomial structure for the Lie algebra is satisfied, it is proved that 2-form flux integrals 
over a proper 2d submanifold are finite and obey the relations 
, where the 
are certain constants (related to dilatonic coupling vectors) and the 
are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, . The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra . Examples of polynomials and fluxes for the Lie algebras 
, 
, 
, 
, 
and 
are presented.
© The Author(s), 2017
