Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras

Abstract

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 $H_s(z)$ 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 $p_s>0$, $s=1,\dots ,n$. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks $n=1,2,3,4,5$ and exceptional algebra $E_6$. 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.

40 pages, 6 figures, LaTex, review paper. Revised version: Remark 2 is added, 4 references are deleted, certain text editing is done

References in corpus (6)

• On multidimensional analogs of Melvin's solution for classical series of Lie algebras
• On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
• On generalized Melvin solution for the Lie algebra $E_6$
• Fluxbrane and S-brane solutions with polynomials related to rank-2 Lie algebras
• Nonabelian solutions in a Melvin magnetic universe
• On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras

Cited by in corpus (1)

• Circular geodesics in the field of double-charged dilatonic black holes