On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra

Abstract

A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra $\mathcal{G}$ is considered. The solution contains a metric, $n$ Abelian 2-forms and $n$ scalar fields, where $n$ is the rank of $\mathcal{G}$. It is governed by a set of $n$ moduli functions $H_s(z)$ 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 $q_s$, $s=1,\dots ,n$. In the case when the conjecture on the polynomial structure for the Lie algebra $\mathcal{G}$ is satisfied, it is proved that 2-form flux integrals ${\Phi }^s$ over a proper $2d$ submanifold are finite and obey the relations: $q_s{\Phi }^s=4\pi n_s{h}_s$, where $h_s>0$ are certain constants (related to dilatonic coupling vectors) and $n_s$ are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, $s=1,\dots ,n$. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra $\mathcal{G}$. Examples of polynomials and fluxes for the Lie algebras $A_1$, $A_2$, $A_3$, $C_2$, $G_2$ and $A_1+A_1$ are presented.

arXiv comment10 pages, Latex, no figures, prepared for a talk at RUSGRAV-16 conference, 2nd revised version, several typos (mainly grammar ones) are eliminated. arXiv admin note: text overlap with arXiv:1706.06621

References in corpus (26)

• 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
• Spacelike Singularities and Hidden Symmetries of Gravity
• 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
• Generalised supersymmetric fluxbranes
• 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
• 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
• Nonabelian solutions in a Melvin magnetic universe

Cited by in corpus (3)

• On generalized Melvin solutions for Lie algebras of rank 3
• Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras
• On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras