SciPost Submission Page
Tripartite information at long distances
by César A. Agón, Pablo Bueno, Horacio Casini
This Submission thread is now published as SciPost Phys. 12, 153 (2022)
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).