Long-distance N-partite information for fermionic CFTs
Abstract The mutual information, I 2, of general spacetime regions is expected to capture the full data of any conformal field theory (CFT). For spherical regions, this data can be accessed from long-distance expansions of the mutual information of pairs of regions as well as of suitably chosen line...
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)178 |
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| author | César A. Agón Pablo Bueno Guido van der Velde |
| author_facet | César A. Agón Pablo Bueno Guido van der Velde |
| author_sort | César A. Agón |
| collection | DOAJ |
| description | Abstract The mutual information, I 2, of general spacetime regions is expected to capture the full data of any conformal field theory (CFT). For spherical regions, this data can be accessed from long-distance expansions of the mutual information of pairs of regions as well as of suitably chosen linear combinations of mutual informations involving more than two regions and their unions — namely, the N-partite information, I N . In particular, the leading term in the I 2 long-distance expansion is fully determined by the spin and conformal dimension of the lowest-dimensional primary of the theory. When the operator is a scalar, an analogous formula for the tripartite information I 3 contains information about the OPE coefficient controlling the fusion of such operator into its conformal family. When it is a fermionic field, the coefficient of the leading term in I 3 vanishes instead. In this paper we present an explicit general formula for the long-distance four-partite information I 4 of general CFTs whose lowest-dimensional operator is a fermion ψ. The result involves a combination of four-point and two-point functions of ψ and ψ ¯ $$ \overline{\psi} $$ evaluated at the locations of the regions. We perform explicit checks of the formula for a (2 + 1)-dimensional free fermion in the lattice finding perfect agreement. The generalization of our result to the N-partite information (for arbitrary N) is also discussed. Similarly to I 3, we argue that I 5 vanishes identically at leading order for general fermionic theories, while the I N with N = 7, 9, … only vanish when the theory is free. |
| format | Article |
| id | doaj-art-499c67c8ad6648ffb9d23eba5b19b0a3 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-499c67c8ad6648ffb9d23eba5b19b0a32025-01-05T12:06:36ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241213010.1007/JHEP12(2024)178Long-distance N-partite information for fermionic CFTsCésar A. Agón0Pablo Bueno1Guido van der Velde2Institute for Theoretical Physics, Utrecht UniversityDepartament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de BarcelonaDepartament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de BarcelonaAbstract The mutual information, I 2, of general spacetime regions is expected to capture the full data of any conformal field theory (CFT). For spherical regions, this data can be accessed from long-distance expansions of the mutual information of pairs of regions as well as of suitably chosen linear combinations of mutual informations involving more than two regions and their unions — namely, the N-partite information, I N . In particular, the leading term in the I 2 long-distance expansion is fully determined by the spin and conformal dimension of the lowest-dimensional primary of the theory. When the operator is a scalar, an analogous formula for the tripartite information I 3 contains information about the OPE coefficient controlling the fusion of such operator into its conformal family. When it is a fermionic field, the coefficient of the leading term in I 3 vanishes instead. In this paper we present an explicit general formula for the long-distance four-partite information I 4 of general CFTs whose lowest-dimensional operator is a fermion ψ. The result involves a combination of four-point and two-point functions of ψ and ψ ¯ $$ \overline{\psi} $$ evaluated at the locations of the regions. We perform explicit checks of the formula for a (2 + 1)-dimensional free fermion in the lattice finding perfect agreement. The generalization of our result to the N-partite information (for arbitrary N) is also discussed. Similarly to I 3, we argue that I 5 vanishes identically at leading order for general fermionic theories, while the I N with N = 7, 9, … only vanish when the theory is free.https://doi.org/10.1007/JHEP12(2024)178Scale and Conformal SymmetriesField Theories in Lower Dimensions |
| spellingShingle | César A. Agón Pablo Bueno Guido van der Velde Long-distance N-partite information for fermionic CFTs Journal of High Energy Physics Scale and Conformal Symmetries Field Theories in Lower Dimensions |
| title | Long-distance N-partite information for fermionic CFTs |
| title_full | Long-distance N-partite information for fermionic CFTs |
| title_fullStr | Long-distance N-partite information for fermionic CFTs |
| title_full_unstemmed | Long-distance N-partite information for fermionic CFTs |
| title_short | Long-distance N-partite information for fermionic CFTs |
| title_sort | long distance n partite information for fermionic cfts |
| topic | Scale and Conformal Symmetries Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP12(2024)178 |
| work_keys_str_mv | AT cesaraagon longdistancenpartiteinformationforfermioniccfts AT pablobueno longdistancenpartiteinformationforfermioniccfts AT guidovandervelde longdistancenpartiteinformationforfermioniccfts |