Composite Fluxbranes with General Intersections

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 M1 × . . . × Mn with 1-dimensional M1 . They are defined up to a set of functions Hs obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions Hs for intersections related to semisimple Lie algebras is suggested. This conjecture is valid for Lie algebras: Am , Cm+1 , m ≥ 1 . 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 A1 ⊕ . . . ⊕ A1 (orthogonal), ”block-ortogonal” and A2 solutions are obtained. Certain examples of solutions in D = 11 and D = 10 ( IIA ) supergravities (e.g. with A2 intersection rules) and Kaluza-Klein dyonic A2 flux tube, are considered. *PACS numbers: 0420J, 0450, 0470 [email protected]