Yangian Ward identities for fishnet four-point integrals
Abstract We derive and study Yangian Ward identities for the infinite class of four-point ladder integrals and their Basso-Dixon generalisations. These symmetry equations follow from interpreting the respective Feynman integrals as correlation functions in the biscalar fishnet theory. Alternatively,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2022)131 |
| _version_ | 1797865847994187776 |
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| author | Luke Corcoran Florian Loebbert Julian Miczajka |
| author_facet | Luke Corcoran Florian Loebbert Julian Miczajka |
| author_sort | Luke Corcoran |
| collection | DOAJ |
| description | Abstract We derive and study Yangian Ward identities for the infinite class of four-point ladder integrals and their Basso-Dixon generalisations. These symmetry equations follow from interpreting the respective Feynman integrals as correlation functions in the biscalar fishnet theory. Alternatively, the presented identities can be understood as anomaly equations for a momentum space conformal symmetry. The Ward identities take the form of inhomogeneous extensions of the partial differential equations defining the Appell hypergeometric functions. We employ a manifestly conformal tensor reduction in order to express these inhomogeneities in compact form, which are given by linear combinations of Basso-Dixon integrals with shifted dimensions and propagator powers. The Ward identities naturally generalise to a one-parameter family of D-dimensional integrals representing correlators in the generalised fishnet theory of Kazakov and Olivucci. When specified to two spacetime dimensions, the Yangian Ward identities decouple. Using separation of variables, we explicitly bootstrap the solution for the conformal 2D box integral. The result is a linear combination of Yangian invariant products of Legendre functions, which reduce to elliptic K integrals for an isotropic choice of propagator powers. We comment on differences in the transcendentality patterns in two and four dimensions and their relations to discontinuities. |
| first_indexed | 2024-04-09T23:14:31Z |
| format | Article |
| id | doaj.art-c75894864c89405390d60ef509b7e286 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:31Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-c75894864c89405390d60ef509b7e2862023-03-22T10:10:23ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022415310.1007/JHEP04(2022)131Yangian Ward identities for fishnet four-point integralsLuke Corcoran0Florian Loebbert1Julian Miczajka2Institut für Physik, Humboldt-Universität zu BerlinInstitut für Physik, Humboldt-Universität zu BerlinMax-Planck-Institut für PhysikAbstract We derive and study Yangian Ward identities for the infinite class of four-point ladder integrals and their Basso-Dixon generalisations. These symmetry equations follow from interpreting the respective Feynman integrals as correlation functions in the biscalar fishnet theory. Alternatively, the presented identities can be understood as anomaly equations for a momentum space conformal symmetry. The Ward identities take the form of inhomogeneous extensions of the partial differential equations defining the Appell hypergeometric functions. We employ a manifestly conformal tensor reduction in order to express these inhomogeneities in compact form, which are given by linear combinations of Basso-Dixon integrals with shifted dimensions and propagator powers. The Ward identities naturally generalise to a one-parameter family of D-dimensional integrals representing correlators in the generalised fishnet theory of Kazakov and Olivucci. When specified to two spacetime dimensions, the Yangian Ward identities decouple. Using separation of variables, we explicitly bootstrap the solution for the conformal 2D box integral. The result is a linear combination of Yangian invariant products of Legendre functions, which reduce to elliptic K integrals for an isotropic choice of propagator powers. We comment on differences in the transcendentality patterns in two and four dimensions and their relations to discontinuities.https://doi.org/10.1007/JHEP04(2022)131AdS-CFT CorrespondenceConformal and W SymmetryIntegrable Field TheoriesQuantum Groups |
| spellingShingle | Luke Corcoran Florian Loebbert Julian Miczajka Yangian Ward identities for fishnet four-point integrals Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Integrable Field Theories Quantum Groups |
| title | Yangian Ward identities for fishnet four-point integrals |
| title_full | Yangian Ward identities for fishnet four-point integrals |
| title_fullStr | Yangian Ward identities for fishnet four-point integrals |
| title_full_unstemmed | Yangian Ward identities for fishnet four-point integrals |
| title_short | Yangian Ward identities for fishnet four-point integrals |
| title_sort | yangian ward identities for fishnet four point integrals |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Integrable Field Theories Quantum Groups |
| url | https://doi.org/10.1007/JHEP04(2022)131 |
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