A violation of global symmetries from replica wormholes and the fate of black hole remnants

TL;DR

The paper argues that replica wormholes in quantum gravity non-perturbatively violate exact global symmetries, demonstrated through explicit charged-state transitions in 2D gravity models and analyzed via planar JT-resummations. It clarifies how global versus gauge symmetries behave under wormhole contributions and connects these insights to holographic factorization, ensemble averaging, and the fate of black-hole remnants. The work latches onto the Page-curve framework to show that a complete charged-state basis can reconstruct interior states once the basis size exceeds $e^{2S_{BH}}$, while still preserving the central dogma for remnants within the ensemble-averaged picture. Overall, it suggests that bulk global symmetries must be broken or emergent only after averaging, whereas bulk gauge symmetries remain robust, with significant implications for holography and UV completions.

Abstract

We show that the presence of replica wormholes in the Euclidean path integral of gravity leads to a non-perturbative violation of charge conservation for any global symmetry present in the low-energy description of quantum gravity. Explicitly, we compute the scattering probability between different charged states in several two-dimensional models of quantum gravity and find a non-vanishing answer. This suggests that the set of all charged states is typically over-complete, which has drastic consequences for the fate of black hole remnants that could carry a global symmetry charge. In the holographic context, we argue that the presence of such a symmetry in the effective description of the bulk should appear on the boundary as an emergent global symmetry after ensemble averaging.

Figures (6)

• Figure 1: The Penrose Diagram of an evaporating black hole. At $\mathcal{I}^-$, we collide a large amount of particles, forming a representation $R$ under the global symmetry $G$, to create a black hole. The Hawking radiation at $\mathcal{J}^+$ is thermal and independent of $R$HAWKING1974Hawking1975. The original matter is stored in the interior region $\mathcal{H}$, which causes a problem when the log of dimension of the representation $R$ exceeds the Bekenstein-Hawking entropy.
• Figure 2: A decomposition of the Euclidean wormhole seen in the second line of \ref{['eq:in-out-2']} into patches on the Poincaré disk.
• Figure 3: The first line shows the leading order contributions when evaluation the matrix $M^n$ needed in order to find null states. The second line shows an example of a subleading in $K$ contribution which is only present when $p_{n-1} = p_{n+1}$. When the basis set of states, given by the charges $p_{j} \in \{q_1,\,\,\dots\,,\,q_K\}$, has a dimension $K> e^{2S_\text{BH}}$, the leading contribution is solely given by the first geometry with all other contributions is suppressed in $K$.
• Figure 4: Spatial section of black hole at late times, decaying into a closed universe.
• Figure 5: The inner product between different states in a closed universe. The brown and blue dots represent insertion of operators with different charges. On the left figure, the inner product between these two states is zero. On the right figure, the fidelity of these two states is equal to one, which means the two states are equivalent up to a phase.