Aspects of N-partite information in conformal field theories
Abstract 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 wh...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2023)246 |
| _version_ | 1797795913682386944 |
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| author | César A. Agón Pablo Bueno Oscar Lasso Andino Alejandro Vilar López |
| author_facet | César A. Agón Pablo Bueno Oscar Lasso Andino Alejandro Vilar López |
| author_sort | César A. Agón |
| collection | DOAJ |
| description | Abstract 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 −2N∆, 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. |
| first_indexed | 2024-03-13T03:25:13Z |
| format | Article |
| id | doaj.art-6a6379e3397944f8a614bcbff2df5e92 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-13T03:25:13Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-6a6379e3397944f8a614bcbff2df5e922023-06-25T11:04:47ZengSpringerOpenJournal of High Energy Physics1029-84792023-03-012023316710.1007/JHEP03(2023)246Aspects of N-partite information in conformal field theoriesCésar A. Agón0Pablo Bueno1Oscar Lasso Andino2Alejandro Vilar López3Instituto Balseiro, Centro Atómico BarilocheTheoretical Physics Department, CERNEscuela de Ciencias Físicas y Matemáticas, Universidad de Las AméricasPhysique Théorique et Mathématique and International Solvay Institutes, Université Libre de BruxellesAbstract 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 −2N∆, 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.https://doi.org/10.1007/JHEP03(2023)246Conformal and W SymmetryField Theories in Higher DimensionsLattice Quantum Field TheoryAdS-CFT Correspondence |
| spellingShingle | César A. Agón Pablo Bueno Oscar Lasso Andino Alejandro Vilar López Aspects of N-partite information in conformal field theories Journal of High Energy Physics Conformal and W Symmetry Field Theories in Higher Dimensions Lattice Quantum Field Theory AdS-CFT Correspondence |
| title | Aspects of N-partite information in conformal field theories |
| title_full | Aspects of N-partite information in conformal field theories |
| title_fullStr | Aspects of N-partite information in conformal field theories |
| title_full_unstemmed | Aspects of N-partite information in conformal field theories |
| title_short | Aspects of N-partite information in conformal field theories |
| title_sort | aspects of n partite information in conformal field theories |
| topic | Conformal and W Symmetry Field Theories in Higher Dimensions Lattice Quantum Field Theory AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP03(2023)246 |
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