On multidimensional analogs of Melvin's solution for classical series of Lie algebras

Details On multidimensional analogs of Melvin's solution for classical series of Lie algebras On multidimensional analogs of Melvin's solution for classical series of Lie algebras

2010-09-19

arxiv.org/abs/1009.3667v1

Grav.Cosmol.15:144-147,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, based on a report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow)

Scientific paper

10.1134/S0202289309020078

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra $\cal G$ is presented. The gravitational model contains n 2-forms and $l \geq n$ scalar fields, wheren is the rank of $\cal G$. 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 of these polynomials for classical series of Lie algebras is suggested (see Appendix). The polynomials corresponding to the Lie algebra D_4 are obtained. It is conjectured that the polynomials for A_n-, B_n- and C_n-series may be obtained from polynomials for D_{n+1}-series by using certain reduction formulas.

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