Tripartite information at long distances

TL;DR

This paper calculates the long-distance behavior of tripartite information in conformal field theories, revealing how it depends on operator dimensions and OPE coefficients, with implications for mutual information monogamy.

Contribution

It provides the leading asymptotic expression for tripartite information in CFTs and explores its dependence on operator data, supported by lattice computations.

Findings

Tripartite information decays as r^{-6Δ} at long distances.

Mutual information monogamy requires large OPE coefficients.

For free fermions, mutual information is non-monogamous at long distances.

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.