Brane Junctions in the Randall-Sundrum Scenario

TL;DR

This work extends the Randall–Sundrum framework to brane junctions formed by intersecting semi-infinite 4-branes in 5+1 dimensions, deriving static solutions by gluing AdS patches and enforcing brane junction conditions. A necessary mechanical balance at the junction, together with specific fine-tuning relations between brane tensions and bulk cosmological constants, governs the existence of these solutions. In two explicit examples—two intersecting 4-branes and a triple junction—the authors derive explicit formulas for the inter-brane angles and the associated tuning conditions, finding that at least one tuning among tensions and λ parameters remains independent of the angles. The paper concludes that, while such configurations illuminate how extra-dimensional geometry can influence 4D physics, they do not provide a dynamical resolution of the cosmological constant problem without further structural or dynamical ingredients; it remains an open challenge to construct setups where angle adjustments alone drive the vanishing of the 4D cosmological constant.

Abstract

We present static solutions to Einstein's equations corresponding to branes at various angles intersecting in a single 3-brane. Such configurations may be useful for building models with localized gravity via the Randall-Sundrum mechanism. We find that such solutions may exist only if the mechanical forces acting on the junction exactly cancel. In addition to this constraint there are further conditions that the parameters of the theory have to satisfy. We find that at least one of these involves only the brane tensions and cosmological constants, and thus can not have a dynamical origin. We present these conditions in detail for two simple examples. We discuss the nature of the cosmological constant problem in the framework of these scenarios, and outline the desired features of the brane configurations which may bring us closer towards the resolution of the cosmological constant problem.

Figures (4)

• Figure 1: A single 3-brane with tension $V$ divides the 4+1 dimensional space-time into two domains with different cosmological constants.
• Figure 2: The setup of semi-infinite 4-branes intersecting in a single 3-brane in 5+1 dimensions. The brane tensions are denoted by $V_i$, while the bulk cosmological constants are given by $\Lambda_i$.
• Figure 3: Two 4-branes with tensions $V_1$ and $V_2$ intersecting at an angle $\varphi$. The four domains may have different cosmological constants.
• Figure 4: Three semi-infinite 4-branes intersecting at angles $\varphi_1$ and $\varphi_2$ in a single 3-brane.