Why would the validity of UV/IR decoupling imply the explicit constructability of black hole remnants?

Question

A paper written in 2020 by Harlow and Shaghoulian (reference 1) proposes a connection between unitary black hole evaporation and the non-existence of global symmetries in quantum gravity. In passing (page 6), they make this statement about a different connection, namely between locality and black hole remnants (which never evaporate):

...Einstein gravity is not renormalizable in $3+1$ dimensions..., and so far the “asymptotic safety” program that looks for a strongly-coupled UV fixed point for Einstein gravity in $3 + 1$ dimensions (such as the proponents of loop quantum gravity hope to find) has been unsuccessful. Moreover even if such a program were successful, the above examples suggest that it would lead to black holes whose entropy is not consistent with the Bekenstein-Hawking formula..., basically because locality would ensure the validity of UV/IR decoupling so one would be able to explicitly construct remnants. ...these remnants would necessarily involve high-energy degrees of freedom in some essential way.

Why would the "validity of UV/IR decoupling" allow us to explicitly construct remnants? Are they merely saying that such a theory would necessarily have remnants? That I could believe. But they seem to be saying that we would automatically be able to explicitly construct those remnants. Is that really what they mean? If so, then how does that follow from the validity of UV/IR decoupling?

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1. Harlow and Shaghoulian, Global symmetry, Euclidean gravity, and the black hole information problem (https://arxiv.org/abs/2010.10539)

Answer 1

Disclaimer: Personally, I am not fully sure about this paper, since it outlines a connection between the Page curve and non-existence of global symmetries. For me, the idea of a Page curve in gravity is a bit difficult to digest since the Hilbert space of gravity doesn't factorize upon spatial partitioning due to the Gauss constraint. However the general arguments can possibly be correct, and there might be connections between unitarity and lack of global symmetries, possibly in some other form.

Now note that a local quantum field theory has the following features:

1. There is no mixing between UV and IR degrees of freedom due to locality.
2. There is no bound on the amount of information you can store in a region. In fact, using a naive calculation one can show that the entanglement entropy diverges even for a bulk scalar field, and one needs to appropriately regulate such quantities.

In a local QFT, the fact that there is no UV/IR mixing along with no bound on information content poses no restriction to the construction of remnant like objects with high information content which cannot be extracted from causally disconnected regions.

However, both these features are violated in a quantum theory of gravity. A drastic violation of the first feature (and locality in general) is the black hole complementarity principle, where the interior degrees of freedom are encoded in the exterior degrees of freedom, i.e., $$O(x_{in}) = P(O(x^1_{out}), O(x^1_{out}), O(x^1_{out})...),$$ where $P$ denotes a polynomial of $O(\mathcal{N})$ where $\mathcal{N}$ is the central charge given by $\mathcal{N}=N^2$, where $N$ is the gauge group of the boundary CFT. Such a description is necessary to consistently resolve no-cloning and strong subadditivity paradoxes.

The second feature is in contrast to the Bekenstein Hawking bound, which is a necessary property of any well-defined quantum theory of gravity. Analogously, there exist nice fine grained RT formula and its generalizations to calculate the entanglement entropy which predict a finite entropy.

This naively indicates that the existence of remnants is ill posed, since their effects would be visible using far-away experiments, and they violate the Bekenstein Hawking entropy. This is yet another argument against remnants, apart from the standard one involving excessive contributions to low energy scattering experiments due to their existence.