Holographic Network and Traversable Parallel Universe

TL;DR

The paper develops a holographic network framework in Gauss-Bonnet gravity with varying bulk branches, deriving node conservation laws from Net-brane junction conditions via a holographic Noether approach. It analyzes KK-mode stability under ghost-free constraints, formulates network entropies that obey the holographic g-theorem, and studies edge correlation functions and RT-surface junctions in compact networks. It further extends to AdS/NCFT scenarios with tensionless Net-branes and AdS$_3$/NCFT$_2$ vacua, and finally presents traversable parallel universes connected by Net-brane junctions that respect energy conditions and causality, including explicit threefold and gravity-bath models. The results provide a versatile, multi-branch holographic toolkit for NCFT networks and speculative but consistent realizations of traversable universes with potential implications for information transfer in quantum gravitational contexts.

Abstract

This paper investigates the holographic network connecting different CFTs, modeled by Gauss-Bonnet gravity with varying couplings across different bulk branches. By applying the holographic Noether's theorem, we prove that the junction condition on the Net-brane leads to conservation laws at network nodes. We analyze the stability of the gravitational KK modes on the Net-brane and derive the constraints on theory parameters. Additionally, we discuss various proposals for network entropy, confirm that the type I and II network entropies obey the holographic g-theorem, and show that the type III network entropy is non-negative. We explore the two-point functions of various NCFTs at different edges, using examples like free scalars and the AdS/NCFT with a tensionless brane. We then examine the gravitational dual of compact networks, which feature both EOW branes and Net-branes in the bulk. We derive the joint condition for EOW branes at the Net-brane and analyze vacuum solutions in AdS$_3$/NCFT$_2$. Finally, we demonstrate that AdS/NCFT provides a natural way to envision traversable parallel universes that have different geometries and physical laws. Remarkably, unlike traversable wormholes, our model of parallel universes satisfies all the energy conditions.

Figures (9)

• Figure 1: The networks with one node (left) and two nodes (right). The blue lines and points denote the edges ($E_m$) and nodes ($N$) of the networks.
• Figure 2: Geometries for holographic networks. The blue lines and points denote the edges ($E_m$) and nodes ($N$) of the networks. The red lines label the Net-branes $NB$, which link the branches $B_m$ (squares) in bulk. The edges ($E_m$) and nodes ($N$) are dual to the branches $B_m$ and Net-branes $NB$ in bulk, respectively. For simplicity, we show only the holographic duals of the networks of Fig. \ref{['network']}. One can glue above geometries to get the gravity duals of general networks.
• Figure 3: The region $V$, where we apply Gauss's law. This region $V$ is outlined by orange lines with red and blue endpoints in the left figure. The length of each orange line approaches zero ($dl \to 0$), and the areas at the red, blue, and green points are all $dS$. In the right figure, we provide more details about $V$, which is bounded by the red, orange, and blue lines. The red, blue, and green points in the left figure correspond to the lines with the same colors in the right figure.
• Figure 4: RT surfaces in AdS/NCFT. The orange lines represent the connected subregion $A$, while the cyan-blue curves indicate the dual RT surfaces $\Gamma$, which remain continuous across the Net-brane in AdS/NCFT. In contrast, the magenta curves corresponding to the RT surfaces $\hat{\Gamma}$ in AdS/BCFT for each bulk branch $B_m$ are usually discontinuous across the Net-brane.
• Figure 5: Network entropies. Without loss of generality, we select the parameters $p = 3$, $\overset{(1)}{L} = 1$, $\overset{(2)}{L} = 2$, $\overset{(3)}{L} = 3$, $4\pi G_{N\ 1} = 3$, $4\pi G_{N\ 2} = 2$, and $4\pi G_{N\ 3} = 1$. It demonstrates that $S_{\text{I}}$ and $S_{\text{II}}$ increase as the tension parameter $\rho$ rises, while $S_{\text{III}}$ decreases. Additionally, $S_{\text{III}}$ remains non-negative (i.e., $S_{\text{III}} \ge 0$), whereas $S_{\text{I}}$ and $S_{\text{II}}$ can be either positive or negative.