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Fishnet Four-point Integrals: Integrable Representations and Thermodynamic Limits by Benjamin Basso; Lance J. Dixon; David A. Kosower; Alexandre Krajenbrink; De-liang Zhong is a Physics and Astronomy article available to read on EtoBox.

What is Fishnet Four-point Integrals: Integrable Representations and Thermodynamic Limits about?

## 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^,

Who reads Fishnet Four-point Integrals: Integrable Representations and Thermodynamic Limits?

Author

Benjamin Basso; Lance J. Dixon; David A. Kosower; Alexandre Krajenbrink; De-liang Zhong

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Physics and Astronomy (Physical Sciences)