Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite entanglement entropy and spectral dimension in quantum gravity   What are the conditions on a field theoretic model leading to a finite
entanglement entropy density? We prove two very general results: 1) Ultraviolet
finiteness of a theory does not guarantee finiteness of the entropy density; 2)
If the spectral dimension of the spatial boundary across which the entropy is
calculated is non-negative at all scales, then the entanglement entropy cannot
be finite. These conclusions, which we verify in several examples, negatively
affect all quantum-gravity models, since their spectral dimension is always
positive. Possible ways out are considered, including abandoning the definition
of the entanglement entropy in terms of the boundary return probability or
admitting an analytic continuation (not a regularization) of the usual
definition. In the second case, one can get a finite entanglement entropy
density in multi-fractional theories and causal dynamical triangulations.

29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin