R\'enyi Mutual Information for Free Scalar in Even Dimensions

TL;DR

This paper calculates the Re9nyi mutual information between two disjoint spheres in free massless scalar theories in even dimensions, using conformal field theory techniques and operator expansions.

Contribution

It provides explicit formulas for Re9nyi mutual information in higher even dimensions, expanding the understanding of entanglement in free scalar conformal field theories.

Findings

Explicit Re9nyi mutual information formulas up to order z^d

Identification of primary operators with minimal dimensions and spins

Expression of mutual information in terms of conformal partial waves

Abstract

We compute the R\'enyi mutual information of two disjoint spheres in free massless scalar theory in even dimensions higher than two. The spherical twist operator in a conformal field theory can be expanded into the sum of local primary operators and their descendants. We analyze the primary operators in the replicated scalar theory and find the ones of the fewest dimensions and spins. We study the one-point function of these operators in the conical geometry and obtain their expansion coefficients in the OPE of spherical twist operators. We show that the R\'enyi mutual information can be expressed in terms of the conformal partial waves. We compute explicitly the R\'enyi mutual information up to order $z^d$, where $z$ is the cross ratio and $d$ is the spacetime dimension.