NS-branes in five-dimensional brane world models

Abstract

We study codimension-1 brane solutions of the five-dimensional brane world models compactified on ${S}_{1}/{\mathbb{Z}}_{2}$. In the string theoretical setup, they suggest that the background branes located at orbifold fixed points should be Neveu-Schwarz (NS)-branes (in the five-dimensional sense), rather than D-branes. Indeed, the existence of the background NS-branes is indispensable to obtain flat geometry ${M}_{4}\ifmmode\times\else\texttimes\fi{}{S}_{1}/{\mathbb{Z}}_{2}$, where ${M}_{4}$ represents the four-dimensional Minkowski spacetime, and without these branes the five-dimensional metric becomes singular everywhere. This result is very reminiscent of the ($p+3$)-dimensional effective string theory [8] where the NS-NS type $p$-brane is indispensable to obtain a flat geometry ${R}_{2}$ or ${R}_{2}/{\mathbb{Z}}_{n}$ on the transverse dimensions. Without this NS-NS type $p$-brane, the two-dimensional transverse space becomes a pin-shaped singular space. The correspondence between these two theories leads us to a conjecture that the whole flat backgrounds of the string theory inherently involve the NS-branes implicitly in their ansatz, and hence the true background $p$-branes immanent in our spacetime may be NS-branes, instead of D-branes. We argue that this result can have a significant consequence in the context of the cosmological constant problem.