Creation of a brane world with a bulk scalar field

TL;DR

This paper explores the creation of brane worlds with a bulk scalar field characterized by an exponential potential, analyzing conditions for instanton solutions and their stability within a supersymmetric theoretical framework.

Contribution

It introduces a model with an exponential bulk scalar potential, connecting supersymmetric theories with brane world creation, and analyzes instanton solutions and their properties.

Findings

Brane instantons exist only for flat branes.

Finite Euclidean action for singular instantons when b2^2 > 2/3.

Singular instantons are well-defined with perturbation analysis.

Abstract

We investigate the creation of a brane world with a bulk scalar field. We consider an exponential potential of a bulk scalar field: $V(\phi)\propto \exp(-2\beta \phi)$, where $\beta$ is the parameter of the theory. This model is based on a supersymmetric theory, and includes the Randall-Sundrum model ($\beta=0$) and the 5-dimensional effective model of the Ho\u{r}va-Witten theory ($\beta=1$). We show that for this potential a brane instanton is constructed only when the curvature of a brane vanishes, that is, the brane is flat. We construct an instanton with two branes and a singular instanton with a single brane. The Euclidean action of the singular instanton solution is finite if $\beta^2 >2/3$. We also calculate perturbations of the action around a singular instanton solution in order to show that the singular instanton is well-defined.