Brane Networks in AdS Space

We present static solutions to Einstein’s equations corresponding to the most general network of $N$ orthogonal families of $(2+N)$-branes in $(4+N)$-dimensional $AdS$ spacetimes. The bulk cosmological constant can take a different value in each cell enclosed by intersecting branes and the extra dimensions can be compact or noncompact. In each family of branes the inter-brane spacing is arbitrary. The extra dimensions may be any or all of the manifolds, $R^1$, $R^1\mathrm{/}{Z}_2$, $S^1$ and $S^1\mathrm{/}{Z}_2$. Only when the extra dimensions are $R^1$ or/and $R^1\mathrm{/}{Z}_2$, can networks consisting solely of positive tension branes be constructed. Such configurations may find application in models with localized gravity and symmetry breaking by shining.