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Article Dans Une Revue Journal of High Energy Physics Année : 2021

Fishnet four-point integrals: integrable representations and thermodynamic limits

Benjamin Basso
Lance J. Dixon
  • Fonction : Auteur
Alexandre Krajenbrink
De-Liang Zhong
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03260073 , version 1 (14-06-2021)

Identifiants

Citer

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, 2021, 07, pp.168. ⟨10.1007/JHEP07(2021)168⟩. ⟨hal-03260073⟩
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