Fishnet four-point integrals: integrable representations and thermodynamic limits
Abstract We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to adm...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2021)168 |
| _version_ | 1819139911974912000 |
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| author | Benjamin Basso Lance J. Dixon David A. Kosower Alexandre Krajenbrink De-liang Zhong |
| author_facet | Benjamin Basso Lance J. Dixon David A. Kosower Alexandre Krajenbrink De-liang Zhong |
| author_sort | Benjamin Basso |
| collection | DOAJ |
| description | Abstract We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS 3 × S 1, in a generalized scaling combining the thermodynamic and short-distance limits. |
| first_indexed | 2024-12-22T11:30:11Z |
| format | Article |
| id | doaj.art-2bb36ab3048a4cfeafb9c9fbfa5c2090 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T11:30:11Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2bb36ab3048a4cfeafb9c9fbfa5c20902022-12-21T18:27:37ZengSpringerOpenJournal of High Energy Physics1029-84792021-07-012021714910.1007/JHEP07(2021)168Fishnet four-point integrals: integrable representations and thermodynamic limitsBenjamin Basso0Lance J. Dixon1David A. Kosower2Alexandre Krajenbrink3De-liang Zhong4Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de ParisSLAC National Accelerator Laboratory, Stanford UniversityInstitut de Physique Théorique, CEA, CNRS, Université Paris-SaclaySISSA and INFNSchool of Physics and Astronomy, Tel Aviv UniversityAbstract We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS 3 × S 1, in a generalized scaling combining the thermodynamic and short-distance limits.https://doi.org/10.1007/JHEP07(2021)168Field Theories in Higher DimensionsIntegrable Field TheoriesScattering Amplitudes |
| spellingShingle | Benjamin Basso Lance J. Dixon David A. Kosower Alexandre Krajenbrink De-liang Zhong Fishnet four-point integrals: integrable representations and thermodynamic limits Journal of High Energy Physics Field Theories in Higher Dimensions Integrable Field Theories Scattering Amplitudes |
| title | Fishnet four-point integrals: integrable representations and thermodynamic limits |
| title_full | Fishnet four-point integrals: integrable representations and thermodynamic limits |
| title_fullStr | Fishnet four-point integrals: integrable representations and thermodynamic limits |
| title_full_unstemmed | Fishnet four-point integrals: integrable representations and thermodynamic limits |
| title_short | Fishnet four-point integrals: integrable representations and thermodynamic limits |
| title_sort | fishnet four point integrals integrable representations and thermodynamic limits |
| topic | Field Theories in Higher Dimensions Integrable Field Theories Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2021)168 |
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