On Brane Solutions Related to Non-Singular Kac-Moody Algebras

TL;DR

This paper reviews multidimensional gravitational models with scalar fields and antisymmetric forms, focusing on solutions involving intersecting branes related to non-singular Kac-Moody algebras, including explicit examples with hyperbolic and Lorentzian algebras.

Contribution

It introduces a sigma-model approach to exact solutions with intersecting branes linked to non-singular Kac-Moody algebras, providing explicit examples and intersection rules.

Findings

Solutions related to hyperbolic Kac-Moody algebras like $H_2(q,q)$, $AE_3$, $HA_2^{(1)}$, $E_{10}$

Explicit examples of intersecting brane solutions

Review of intersection rules connected to non-singular Kac-Moody algebras

Abstract

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form $M = M_0 \times M_1 \times \cdots \times M_n$, where $M_i$ are Einstein spaces ($i \geq 1$). The sigma-model approach and exact solutions with intersecting composite branes (e.g. solutions with harmonic functions, $S$-brane and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are reviewed. Some examples of solutions, e.g. corresponding to hyperbolic KM algebras: $H_2(q,q)$, $AE_3$, $HA_2^{(1)}$, $E_{10}$ and Lorentzian KM algebra $P_{10}$ are presented.