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.

arXiv comment40 pages, 6 figures, LaTex, review paper. Revised version: Remark 2 is added, 4 references are deleted, certain text editing is done

References in corpus (32)

• Pair Creation of Dilaton Black Holes
• Spacetime as a membrane in higher dimensions
• On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles
• Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory
• The Decay of Magnetic Fields in Kaluza-Klein Theory
• Fluxbranes in String Theory
• Nucleation of $P$-Branes and Fundamental Strings
• The Kaluza-Klein Melvin Solution in M-theory
• Multidimensional Classical and Quantum Cosmology with Intersecting p-branes
• Generating branes via sigma-models
• Tubular Branes in Fluxbranes
• Flux-branes and the Dielectric Effect in String Theory
• Exact solutions in multidimensional gravity with antisymmetric forms
• Gravitating Fluxbranes
• A note on the Supergravity Description of Dielectric Branes
• From p-branes to fluxbranes and back
• Supersymmetric fluxbrane intersections and closed string tachyons
• Toda p-brane black holes and polynomials related to Lie algebras
• Composite fluxbranes with general intersections
• Supergravity Fluxbranes in Various Dimensions
• Black brane solutions governed by fluxbrane polynomials
• Dilatonic dyon-like black hole solutions in the model with two Abelian gauge fields
• Fluxbranes from p-branes
• On multidimensional analogs of Melvin's solution for classical series of Lie algebras
• Higher-$n$ triangular dilatonic black holes
• On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
• Discreteness of dyonic dilaton black holes
• On generalized Melvin solution for the Lie algebra $E_6$
• On generalized Melvin solutions for Lie algebras of rank 3
• 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

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