Checkerboard CFT
Abstract The Checkerboard conformal field theory is an interesting representative of a large class of non-unitary, logarithmic Fishnet CFTs (FCFT) in arbitrary dimension which have been intensively studied in the last years. Its planar Feynman graphs have the structure of a regular square lattice wi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)015 |
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| _version_ | 1832595065172656128 |
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| author | Mikhail Alfimov Gwenaël Ferrando Vladimir Kazakov Enrico Olivucci |
| author_facet | Mikhail Alfimov Gwenaël Ferrando Vladimir Kazakov Enrico Olivucci |
| author_sort | Mikhail Alfimov |
| collection | DOAJ |
| description | Abstract The Checkerboard conformal field theory is an interesting representative of a large class of non-unitary, logarithmic Fishnet CFTs (FCFT) in arbitrary dimension which have been intensively studied in the last years. Its planar Feynman graphs have the structure of a regular square lattice with checkerboard colouring. Such graphs are integrable since each coloured cell of the lattice is equal to an R-matrix in the principal series representations of the conformal group. We compute perturbatively and numerically the anomalous dimension of the shortest single-trace operator in two reductions of the Checkerboard CFT: the first one corresponds to the Fishnet limit of the twisted ABJM theory in 3D, whereas the spectrum in the second, 2D reduction contains the energy of the BFKL Pomeron. We derive an analytic expression for the Checkerboard analogues of Basso-Dixon 4-point functions, as well as for the class of Diamond-type 4-point graphs with disc topology. The properties of the latter are studied in terms of OPE for operators with open indices. We prove that the spectrum of the theory receives corrections only at even orders in the loop expansion and we conjecture such a modification of Checkerboard CFT where quantum corrections occur only with a given periodicity in the loop order. |
| format | Article |
| id | doaj-art-aa6af81158e447798528113c12044db8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-aa6af81158e447798528113c12044db82025-01-19T12:07:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025116210.1007/JHEP01(2025)015Checkerboard CFTMikhail Alfimov0Gwenaël Ferrando1Vladimir Kazakov2Enrico Olivucci3HSE UniversitySchool of Physics and Astronomy, Tel Aviv UniversityLaboratoire de Physique de l’École Normale Supériéure, CNRS, Université PSL, Sorbonne Université, Université Paris CitéPerimeter Institute for Theoretical PhysicsAbstract The Checkerboard conformal field theory is an interesting representative of a large class of non-unitary, logarithmic Fishnet CFTs (FCFT) in arbitrary dimension which have been intensively studied in the last years. Its planar Feynman graphs have the structure of a regular square lattice with checkerboard colouring. Such graphs are integrable since each coloured cell of the lattice is equal to an R-matrix in the principal series representations of the conformal group. We compute perturbatively and numerically the anomalous dimension of the shortest single-trace operator in two reductions of the Checkerboard CFT: the first one corresponds to the Fishnet limit of the twisted ABJM theory in 3D, whereas the spectrum in the second, 2D reduction contains the energy of the BFKL Pomeron. We derive an analytic expression for the Checkerboard analogues of Basso-Dixon 4-point functions, as well as for the class of Diamond-type 4-point graphs with disc topology. The properties of the latter are studied in terms of OPE for operators with open indices. We prove that the spectrum of the theory receives corrections only at even orders in the loop expansion and we conjecture such a modification of Checkerboard CFT where quantum corrections occur only with a given periodicity in the loop order.https://doi.org/10.1007/JHEP01(2025)015Integrable Field TheoriesScale and Conformal Symmetries |
| spellingShingle | Mikhail Alfimov Gwenaël Ferrando Vladimir Kazakov Enrico Olivucci Checkerboard CFT Journal of High Energy Physics Integrable Field Theories Scale and Conformal Symmetries |
| title | Checkerboard CFT |
| title_full | Checkerboard CFT |
| title_fullStr | Checkerboard CFT |
| title_full_unstemmed | Checkerboard CFT |
| title_short | Checkerboard CFT |
| title_sort | checkerboard cft |
| topic | Integrable Field Theories Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP01(2025)015 |
| work_keys_str_mv | AT mikhailalfimov checkerboardcft AT gwenaelferrando checkerboardcft AT vladimirkazakov checkerboardcft AT enricoolivucci checkerboardcft |