What is the dual of two entangled CFTs?

TL;DR

The paper critically examines whether the eternal AdS black hole, dual to two entangled CFTs, can remain a valid semiclassical spacetime given Hawking radiation. It contrasts the wormhole (ER=EPR) view with the fuzzball proposal, arguing that Hawking-induced entanglement and entropy considerations undermine a simple connected-bulk dual (P1') while supporting two entangled but disconnected bulk spacetimes (P2') with approximate interior emergence only for high-energy probes via fuzzball complementarity. A central proposal is the quick tunneling conjecture, which posits that geometries with mass confined to $r<2M$ rapidly tunnel to fuzzball states, thereby destroying the interior and resolving the left-right and entropy puzzles. The work thus reframes the dual of two entangled CFTs as two entangled but disconnected spacetimes, with interior phenomena captured only in an approximate, energy-dependent fashion, and highlights the significance for the firewall debate and the understanding of AdS/CFT duality. The findings have broad implications for how information, entanglement, and horizon structure are reconciled in quantum gravity, suggesting that fuzzball dynamics provide a consistent resolution to the information puzzle without requiring a semiclassical eternal wormhole.

Abstract

It has been conjectured that the dual of the eternal black hole in AdS is two entangled but disconnected CFTs. We show that the entanglement created by the process of Hawking radiation creates several challenges for this conjecture. The nature of fuzzball states suggests a different picture, where the dual to two entangled CFTs is two entangled but disconnected spacetimes. We argue for a process of `quick tunneling' where the Einstein-Rosen bridge of the eternal hole tunnels rapidly into fuzzball states, preventing the existence of the eternal hole as a semiclassical spacetime. The regions behind the horizon then emerge only in the approximation of fuzzball complementarity, where one considers the impact of probes with energy $E\gg T$.

Figures (11)

• Figure 1: The conjecture of eternal says that two entangled CFTs (a) gives the connected spacetime (b). The nature of fuzzballs suggests that two entangled CFTs (c) give two entangled but disconnected spacetimes (d).
• Figure 2: (a) The eternal hole in AdS, where Hawking radiation quanta reflect off the boundary and fall back into the hole. (b) We can extract the radiated quanta out to external regions $O_L, O_R$ by applying suitable operators at the boundary.
• Figure 3: Hawking quanta b, c are produced at the horizon. The quanta b are extracted to the external region, while the c fall into the singularity. To restore the mass of the hole, we send in quanta a, which we can entangle beforehand with quanta d that stay in the exterior region.
• Figure 4: (a) In the picture of maldasuss2, we can imagine thin wormholes connecting the entangled pairs b,c and a,d. (b) If the dynamics of wormholes is such that the entanglement moves to b,d, then we may be able to avoid the contradiction (\ref{['contra']}).
• Figure 5: (a) A good slicing of the single sided Schwarzschild hole; the slices are depicted in Eddington-Finkelstein coordinates. (b) The entangled quanta $b_i, c_i$ on the good slice; the quanta $a_i$ on this slice are infalling quanta that maintain the mass of the hole.