Abstract
We study quantum corrections to holographic mutual information for two disjoint spheres at a large separation by using the operator product expansion of the twist field. In the large separation limit, the holographic mutual information is vanishing at the semiclassical order, but receive quantum corrections from the fluctuations. We show that the leading contributions from the quantum fluctuations take universal forms as suggested from the boundary CFT. We find the universal behavior for the scalar, the vector, the tensor and the fermionic fields by treating these fields as free fields propagating in the fixed background and by using the 1/n prescription. In particular, for the fields with gauge symmetries, including the massless vector boson and massless graviton, we find that the gauge parts in the propagators play an indispensable role in reading the leading order corrections to the bulk mutual information.
Highlights
Provided that the continuation on n is well-defined
We study quantum corrections to holographic mutual information for two disjoint spheres at a large separation by using the operator product expansion of the twist field
As we are interested in the mutual information, we can safely ignore the backreaction of the twist operator to the geometry
Summary
Let us consider the mutual information of two disjoint spheres in a d-dimensional CFT. The coefficient s∆,J is given by s∆,J f∆,J. where the summation is over all the primary operators with the same (∆, J) in the replicated theory, a∆,J is determined by the one-point function of the operator O∆,J in the planar conical geometry. The leading contribution to the mutual information is from the primary operator with the lowest dimension and nonvanishing coefficient. It is remarkable that the coefficients for the leading contributions take universal forms, which means that they depend only the scaling dimensions and the spins of the primary operators and have nothing to do with the construction of the CFT itself. One cannot expect to get such universal behaviors as the one-point function of the primary operator in a conical space cannot be determined in a simple way. The coefficient (2.16) was first derived in [36]
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