Composite fluxbranes with general intersections

TL;DR

This paper develops generalized composite fluxbrane solutions with complex intersection rules, linking their structure to Toda-type equations and Lie algebra properties, and provides explicit formulas and examples in supergravity theories.

Contribution

It introduces a broad class of fluxbrane solutions defined by Toda-type equations, conjectures a polynomial structure related to Lie algebras, and derives explicit solutions for specific cases.

Findings

Solutions are characterized by functions obeying Toda-type equations.

A conjecture links polynomial solutions to semisimple Lie algebra structures.

Explicit solutions are provided for A_1, A_2, and block-orthogonal cases.

Abstract

Generalized composite fluxbrane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold which contains a product of n Ricci-flat spaces M_1 x ... x M_n with 1-dimensional M_1. They are defined up to a set of functions H_s obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions H_s for intersections related to semisimple Lie algebras is suggested. This conjecture is valid for Lie algebras: A_m, C_{m+1}, m > 0. For simple Lie algebras the powers of polynomials coincide with the components of the dual Weyl vector in the basis of simple roots. Explicit formulas for A_1 + ... + A_1 (orthogonal), "block-ortogonal" and A_2 solutions are obtained. Certain examples of solutions in D = 11 and D =10 (II A) supergravities (e.g. with A_2 intersection rules) and Kaluza-Klein dyonic A_2 flux tube, are considered.