Creation of a brane world with a bulk scalar field

Abstract

We investigate the creation of a brane world with a bulk scalar field. We consider an exponential potential of a bulk scalar field: $V(ϕ)\propto \exp(-2βϕ)$, where $β$ is the parameter of the theory. This model is based on a supersymmetric theory, and includes the Randall-Sundrum model ($β=0$) and the 5-dimensional effective model of the Hourva-Witten theory ($β=1$). 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 $β^2 >2/3$. We also calculate perturbations of the action around a singular instanton solution in order to show that the singular instanton is well-defined.