Rényi Mutual Information for Free Scalar in Even Dimensions

Abstract

We compute the Rényi 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 Rényi mutual information can be expressed in terms of the conformal partial waves. We compute explicitly the Rényi mutual information up to order $z^d$, where $z$ is the cross ratio and $d$ is the spacetime dimension.

29 pages; More discussion on the partition function of primary operators, the contribution from spin-1 operator has been corrected

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• Correlation function with the insertion of zero modes of modular Hamiltonians
• Is the EMI model a QFT? An inquiry on the space of allowed entropy functions