On multidimensional analogs of Melvin's solution for classical series of Lie algebras
A.A. Golubtsova1 and V.D. Ivashchuk2
(1) Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, Miklukho-Maklaya St. 6, Moscow 117198, Russia
(2) Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, Miklukho-Maklaya St. 6, Moscow 117198, Russia
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is presented. The gravitational model contains n 2-forms and l ³ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions obeying n ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating these polynomials for classical series of Lie algebras is suggested. The polynomials corresponding to the Lie algebra D4 are obtained. It is conjectured that the polynomials for An-,Bn- and Cn- series may be obtained from polynomials for Dn+1-series by using certain reduction formulas.
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