Black brane solutions related to non-singular Kac-Moody algebras

TL;DR

This paper explores black brane solutions within a multidimensional gravitational framework involving scalar fields and antisymmetric forms, utilizing Kac-Moody algebra structures to classify intersecting branes and present explicit solutions.

Contribution

It introduces a sigma-model approach to derive exact intersecting brane solutions linked to non-singular Kac-Moody algebras, expanding the understanding of black branes in higher-dimensional theories.

Findings

Constructed explicit black brane solutions related to hyperbolic Kac-Moody algebras.

Demonstrated intersection rules governed by non-singular Kac-Moody algebra structures.

Provided examples involving hyperbolic and Lorentzian 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 x M_1 x ... x M_n, where M_i are Einstein spaces (i > 0). The sigma-model approach and exact solutions with intersecting composite branes (e.g., solutions with harmonic functions and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are considered. Some examples of black brane solutions are presented, e.g., those corresponding to hyperbolic KM algebras: H_2(q,q) (q > 2), HA_2^(1) = A_2^{++} and to the Lorentzian KM algebra P_{10}.