Fishnet four-point integrals: integrable representations and thermodynamic limits
Abstract
In this work, 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 AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.
- Authors:
-
[5]
- Laboratoire de Physique de l’Ecole Normale Supérieure, Paris (France); Univ. Paris Sciences et Lettres (PSL), Paris (France)
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Univ. Paris-Saclay, Gif-sur-Yvette (France). Institut de Physique Théorique
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Trieste (Italy)
- Tel Aviv Univ., Ramat Aviv (Israel)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); French National Agency for Research; Israel Science Foundation
- OSTI Identifier:
- 1819720
- Alternate Identifier(s):
- OSTI ID: 1819315
- Grant/Contract Number:
- AC02-76SF00515; ANR-17-CE31-0001-01; ANR-17-CE31-0001-0; PHY-1748958; ANR-17-CE30-0027-012; 771536; 2289/18; 1197/20
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 7; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Field Theories in Higher Dimensions, Integrable Field Theories, Scattering Amplitudes
Citation Formats
Basso, Benjamin, Dixon, Lance J., Kosower, David A., Krajenbrink, Alexandre, and Zhong, De-liang. Fishnet four-point integrals: integrable representations and thermodynamic limits. United States: N. p., 2021.
Web. doi:10.1007/jhep07(2021)168.
Basso, Benjamin, Dixon, Lance J., Kosower, David A., Krajenbrink, Alexandre, & Zhong, De-liang. Fishnet four-point integrals: integrable representations and thermodynamic limits. United States. https://doi.org/10.1007/jhep07(2021)168
Basso, Benjamin, Dixon, Lance J., Kosower, David A., Krajenbrink, Alexandre, and Zhong, De-liang. Thu .
"Fishnet four-point integrals: integrable representations and thermodynamic limits". United States. https://doi.org/10.1007/jhep07(2021)168. https://www.osti.gov/servlets/purl/1819720.
@article{osti_1819720,
title = {Fishnet four-point integrals: integrable representations and thermodynamic limits},
author = {Basso, Benjamin and Dixon, Lance J. and Kosower, David A. and Krajenbrink, Alexandre and Zhong, De-liang},
abstractNote = {In this work, 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 AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.},
doi = {10.1007/jhep07(2021)168},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2021,
place = {United States},
year = {Thu Jul 22 00:00:00 EDT 2021},
month = {Thu Jul 22 00:00:00 EDT 2021}
}
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