The Replica Trick, Wormholes, Island formula, and Quantum Extremal Surfaces, and How the AdS/CFT Correspondence Conjecture, and Hence the M-theory, Encounters Multi-folds
Authors: Maes Stephane 
Published: November 2023

The multi-fold theory factually encounters the AdS/CFT correspondence conjecture: the AdS(5) space is tangent dual to the multi-fold spacetime. On the other hand, while the derivation of the conventional conjecture involved branes in AdS(5) (+ …), which amounts to physical dual tangency, and key derivations like the Ryu–Takayanagi conjecture, are based on the same model, the conventional AdS/CFT correspondence conjecture can also be understood as a mathematical duality, where the CFT spacetime is not necessarily physically tangent to AdS(5) (+…). It can be justified as a particular case of the holographic principle. Therefore, the paper will revisit, and derive the holographic principle, in a multi-fold universe. As General relativity (GR) encounters multi-folds at Planck scales, the proof applies to GR-based universes. We also debunk the use of Wheeler’s bag of gold as a counter example to the holographic principle.Trying to resolve the black hole information paradox, different teams have been able to recover the black hole Page curve, by relying on the replica trick with generalized semi-classical gravitational path integrals, in asymptotic AdS, with arbitrary topologies, including spacetime (Euclidian) wormholes in between replicas, to justifies paths in between the replicas. The approach also relies on the island formula for the von Neuman entropy as fine-grained entropy. One knows that the Page curve had to be recovered one way or another as with the AdS/CFT correspondence conjecture, the unitarity of CFTs implies unitarity of gravity. The results, have also been extended to de Sitter asymptotic spacetime. The quantum extremal surface that appears in the process, bounding the island, leads to proposed physical interpretations of a black hole interior, that, in our opinion lead to more confusions than answers. In the multi-fold theory, we have already encountered an equivalent surface, with a much cleaner microscopic interpretation. For this paper, all what matters is that the microscopic interpretation validates the approach of replica tick, wormholes and island. But on the way, the paper discusses the differences between the multi-fold model and the conventional interpretation. A few recent papers reused the approach to study two entangled gravitating universes, with one possibly without gravity. Admittedly, speaking of different universes is a bit of an oxymoron, as a universe embodies everything that is physical. Also, what is between universes, whatever that means, seems even more a red herring, unless if they were to share, or be a (global) embedding or dual tangent space that is physical. Phrased this way, the holographic AdS/CFT correspondence conjecture would be a particular case. The papers also rely on the replica trick, and its wormholes, adding some replica and wormholes swapping entangled universe parts. They recovers sensible, and unitary behaviors as well as the ER = EPR conjecture. This paper provides multi-fold inspired interpretations of the quantum extremal surfaces appearing among the disjoint universes.Interpreting the replica trick, and its wormholes, in both the cases of black holes and entangled disjoint universes, one can see that the role played by the wormholes between different replicas amounts to the multi-fold mechanisms.. This is further reinforced by considerations on global symmetry in the presence of gravity or wormholes. The islands associated to the different entangled universe use cases also imply that, in universes with gravity, entanglement implies gravity effects, which is also known as the E/G conjecture, factual in multi-fold theory. With the (disjoint) AdS/CFT conjecture, this means that it, and therefore the M-theory encounters multi-folds. The multi-fold theory could have predicted such an outcome from the link between the Hilbert Einstein action and superstring action, and the fact that we already had GR encounter multi-folds at Planck scales.