Creation of a brane world with a bulk scalar field

We investigate a creation of a brane world with a bulk scalar field. We consider an exponential potential of a bulk scalar field; V(φ) ∝ (-2βφ), where β is the parameter of the theory. This model is based on a supersymmetric theory, and includes Randall-Sundrum model (β = 0) and the 5-dimensional effective model of the Horva-Witten theory (β = 1). We show that for this potential a brane instanton is constructed only when a 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 β² > 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.