Fractional black $p$-branes on orbifold ${\mathbb C}^n/{\mathbb Z}_n$

TL;DR

This paper constructs explicit extremal black p-brane solutions on orbifolds ${\mathbb C}^n/{\mathbb Z}_n$, confirming their regular horizons and near-horizon geometries, advancing understanding of branes in orbifold backgrounds.

Contribution

It provides explicit solutions for black p-branes on orbifolds, verifying their regularity and near-horizon structure, which was previously predicted but not explicitly demonstrated.

Findings

Black p-branes on ${\mathbb C}^n/{\mathbb Z}_n$ have regular horizons.

Near horizon geometries are AdS${}_{p+2}\times S^{2n-1}/{\mathbb Z}_n$.

Solutions confirm the existence of extremal black branes on orbifolds.

Abstract

The recent discovery of an explicit solution of a black hole on the resolved orbifold ${\mathbb C}^n/{\mathbb Z}_n$ makes it possible to investigate the existence of $p$-branes on the orbifold. In particular, it is possible with reasonable precision to verify the prediction that an M2-brane on ${\mathbb C}^4/{\mathbb Z}_4$ in eleven dimensions and a D3-brane on ${\mathbb C}^3/{\mathbb Z}_3$ in ten dimensions have a family of black $p$-branes on the orbifold ${\mathbb C}^n/{\mathbb Z}_n$. These solutions are extremal and have regular horizons $S^{2n-1}/{\mathbb Z}_n$ without any naked singularity, with near horizon geometries AdS${}_{p+2}\times S^{2n-1}/{\mathbb Z}_n$.