Lessons on Eternal Traversable Wormholes in AdS

TL;DR

The paper investigates whether eternal traversable wormholes can exist between two asymptotically AdS regions by coupling the dual CFTs with a static double-trace deformation. Under a Poincaré-invariant ansatz and Weyl-invariant NEC-violating matter, the analysis shows a no-go for semiclassical wormholes in dimensions higher than two, due to Planckian curvature, Weyl anomaly, Casimir energy, and quantum-energy inequalities. The authors also assess strategies to evade the no-go, including adding bulk matter or introducing a large number of fields, and conclude that these approaches either fail or encounter non-perturbative UV-cutoff constraints and the no-transmission principle. They suggest exploring less symmetric configurations or alternative NEC-violating ingredients as promising directions. Overall, the work delineates the limitations of static, Poincaré-invariant AdS wormholes and outlines plausible avenues for future constructions beyond the highly symmetric setup.

Abstract

We attempt to construct eternal traversable wormholes connecting two asymptotically AdS regions by introducing a static coupling between their dual CFTs. We prove that there are no semiclassical traversable wormholes with Poincaré invariance in the boundary directions in higher than two spacetime dimensions. We critically examine the possibility of evading our result by coupling a large number of bulk fields. Static, traversable wormholes with less symmetry may be possible, and could be constructed using the ingredients we develop here.

Figures (4)

• Figure 1: Typical shape of the potential $V(a)$ and the conformal factor for a wormhole solution $a(z)$. For the plots we have set $\ell_{\text{AdS}}=1$ and we have set $a(0)=1$.
• Figure 2: Left: Shape of the potential $V(\phi)$. Right: The corresponding solution. We are using Planck units for the two plots.
• Figure 3: We plot $\lambda$ as a function of $\ell_{\text{AdS}}$ while varying $V_0$ in the interval $-1\leq V_0\leq -10^{-4}$ and we use Planck units. The different curves correspond to different choices for the other parameters in the potential. Left:$m_0=c=10^{-1}$ (blue), $m_0=c=10^{-2}$ (red). Right:$c=10^{-i}$ with $i=2,3$ and $m_0=10^{-1}c$ (blue) and $m_0=10^{-2}c$ (red). The series corresponding to different values of $i$ are indistinguishable. It's impossible to have $\lambda \ll 1$ if we want $\ell_\text{AdS}$ to be large in Planck units.
• Figure 4: We assume that the new term in the Einstein equation dominates up to some $z=z_{*}$, for which we have $a(z_{*})=a_*$. After this value the cosmological constant dominates.