Some results on the mutual information of disjoint regions in higher dimensions

By J. Cardy. 2013

143 citations recorded by the source corpus.

We consider the mutual Rényi information I(n)(A,B)≡SA(n)+SB(n)−SA∪B(n)?> of disjoint compact spatial regions A and B in the ground state of a d + 1-dimensional conformal field theory (CFT), in the limit when the separation r between A and B is much greater than their sizes RA, B. We show that in general I(n)(A,B)∼CA(n)CB(n)(RARB/r2)α?>, where α is the smallest sum of the scaling dimensions of operators whose product has the quantum numbers of the vacuum, and the constants CA,B(n)?> depend only on the shape of the regions and universal data of the CFT. For a free massless scalar field, where α = d − 1, we show that CA(2)RAd−1?> is proportional to the capacitance of a thin conducting slab in the shape of A in d + 1-dimensional electrostatics, and give explicit formulae for this when A is the interior of a sphere Sd − 1 or an ellipsoid. For spherical regions in d = 2 and 3 we obtain explicit results for C(n) for all n and hence for the leading term in the mutual information by taking n → 1. We also compute a universal logarithmic correction to the area law for the Rényi entropies of a single spherical region for a scalar field theory with a small mass.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7494261f83f395dd5789a3827c7c0067bbf56a51

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