Aspects of N-partite information in conformal field theories

• Published in: The journal of high energy physics Vol. 2023; no. 3; pp. 246 - 67
• Main Authors: Agón, César A., Bueno, Pablo, Andino, Oscar Lasso, López, Alejandro Vilar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 30.03.2023; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; Conformal and W Symmetry; Elementary Particles; Entanglement; Entropy; Fermions; Field Theories in Higher Dimensions; High energy physics; Lattice Quantum Field Theory; Lattice theory; Monogamy; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; Spacetime; String Theory; Lattice Quantum Field Theory; AdS-CFT Correspondence; Field Theories in Higher Dimensions; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2023)246

A bstract We present several new results for the N -partite information, I N , of spatial regions in the ground state of d -dimensional conformal field theories. First, we show that I N can be written in terms of a single N -point function of twist operators. Using this, we argue that in the limit in which all mutual separations are much greater than the regions sizes, the N -partite information scales as I N ~ r − 2 N ∆ , where r is the typical distance between pairs of regions and ∆ is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the I 4 in terms of 2-, 3- and 4-point functions of the lowest-dimensional primary. Then, we consider a three- dimensional scalar field in the lattice. We verify the predicted long-distance scaling and provide strong evidence that I N is always positive for general regions and arbitrary N for that theory. For the I 4 , we find excellent numerical agreement between our general formula and the lattice result for disk regions. We also perform lattice calculations of the mutual information for more general regions and general separations both for a free scalar and a free fermion, and conjecture that, normalized by the corresponding disk entanglement entropy coefficients, the scalar result is always greater than the fermion one. Finally, we verify explicitly the equality between the N -partite information of bulk and boundary fields in holographic theories for spherical entangling surfaces in general dimensions.