Footballs, Conical Singularities and the Liouville Equation

TL;DR

This paper extends the football-shaped extra dimensions model to multiple branes, solving the Liouville equation with singularities and providing explicit solutions for three branes, with relaxed tension tuning constraints.

Contribution

It generalizes the football-shaped extra dimensions scenario to an arbitrary number of branes and offers explicit solutions for three branes without fine-tuning tensions.

Findings

Explicit solutions for three-brane configurations.

Brane tensions only need to satisfy global constraints, not fine-tuning.

Generalization to multiple branes in extra-dimensional models.

Abstract

We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.