Holographic Network, Entanglement Wedge and Traversable Parallel Universe

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 find that zero tension results in negative reflectivity at the node, indicating that it is a non-unitary parameter. We study the wedge inclusion condition, which stipulates that the entanglement wedge must encompass the causal wedge. This condition imposes a lower bound on the tension of the Net-brane, which is stronger than the bound derived from the positivity of reflectivity. Furthermore, we conclude that the tension of Net-branes must be positive; the more edges present, the stronger this bound becomes. 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.