Signature change as phase transition in holography

TL;DR

This paper explores how Euclidean regions in holographic spacetimes relate to entangled states, proposing that phase transitions in these geometries correspond to changes in spacetime topology and stability.

Contribution

It extends the ER-EPR conjecture by analyzing how Euclidean regions and phase transitions in holography reflect entanglement and spacetime connectivity.

Findings

Euclidean regions are essential for classical connectivity in holography.

Phase transitions can change the topology of spacetime geometries.

Entanglement persists even when wormholes become unstable.

Abstract

In holographic quantum gravity, Euclidean pieces of the spacetime appear in the large N limit as representing semi-classical states of the theory. In this essay, we argue that the duals of entangled states are spacetime geometries that contain Euclidean regions in order to preserve classical connectivity. Thereby, the proposal is to extend the ER-EPR conjecture to regimes whether wormholes (Einstein-Rosen bridges) become unstable but the entangled structure of the dual state persists.