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Tripartite information at long distances
by César A. Agón, Pablo Bueno, Horacio Casini
This Submission thread is now published as
Submission summary
| As Contributors: | Cesar Agon · Pablo Bueno |
| Arxiv Link: | https://arxiv.org/abs/2109.09179v2 (pdf) |
| Date accepted: | 2022-04-22 |
| Date submitted: | 2022-03-17 05:06 |
| Submitted by: | Agon, Cesar |
| Submitted to: | SciPost Physics |
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We compute the leading term of the tripartite information at long distances for three spheres in a CFT. This falls as $r^{-6\Delta}$, where $r$ is the typical distance between the spheres, and $\Delta$, the lowest primary field dimension. The coefficient turns out to be a combination of terms coming from the two- and three-point functions and depends on the OPE coefficient of the field. We check the result with three-dimensional free scalars in the lattice finding excellent agreement. When the lowest-dimensional field is a scalar, we find that the mutual information can be monogamous only for quite large OPE coefficients, far away from a perturbative regime. When the lowest-dimensional primary is a fermion, we argue that the scaling must always be faster than $r^{-6\Delta_f}$. In particular, lattice calculations suggest a leading scaling $ r^{-(6\Delta_f+1)}$. For free fermions in three dimensions, we show that mutual information is also non-monogamous in the long-distance regime.
Published as SciPost Phys. 12, 153 (2022)
List of changes
From report 1:
We corrected Eq. (20). Changed spurious + sign to a $\times$ sign
From report 2:
We added reference [7] (arXiv:1011.5482) in the second paragraph of page 2 to appropriately cite the coefficient in the long-distance mutual information of disjoint intervals in CFT (spheres in $d=2$). In this regard, we added some extra comments in footnote 2, appearing on page 5.
We added a paragraph on page 9 (the last paragraph of the page), where we explain the prospects of comparing our long-distance tripartite information result Eq (34) with the exact results in $d=2$ presented in references [28] (arXiv:1309.2189) and [29] (arXiv:1501.04311).