Randall-Sundrum scenario with an extra warped dimension

We investigate a scenario with two four branes embedded in six dimensions. When the metric is periodic and compact in one of the dimensions parallel to the branes, the value of the effective cosmological constant for the remaining five dimensions can assume a variety of values, determined by the dependence of the metric on the sixth dimension. The picture that emerges resembles the Randall-Sundrum model but with an extra warped dimension that allows the usual brane-bulk fine tuning to be satisfied without finely tuning any of the parameters in the underlying six-dimensional theory. Although the action contains terms with four derivatives of the metric, we show that when the branes have a finite, natural thickness, such terms have only a small effect on the Randall-Sundrum structure. The presence of these four derivative terms also allows a configuration that resembles that produced by a domain wall but which results from gravity alone.