Light-cone limits of large rectangular fishnets

Abstract

Basso-Dixon integrals evaluate rectangular fishnets -- Feynman graphs with massless scalar propagators which form a $m\times n$ rectangular grid -- which arise in certain one-trace four-point correlators in the `fishnet' limit of $\mathcal{N}=4$ SYM. Recently, Basso {\it et al} explored the thermodynamical limit $m\to \infty$ with fixed aspect ratio $n/m$ of a rectangular fishnet and showed that in general the dependence on the coordinates of the four operators is erased, but it reappears in a scaling limit with two of the operators getting close in a controlled way. In this note I investigate the most general double scaling limit which describes the thermodynamics when one of two pairs of operators become nearly light-like. In this double scaling limit, the rectangular fishnet depends on both coordinate cross ratios. I show that all singular limits of the fishnet can be attained within the double scaling limit, including the null limit with the four points approaching the cusps of a null square. A direct evaluation of the fishnet in the null limit is presented any $m$ and $n$.

24 pages, 5 figures, references added

References in corpus (7)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Logarithmic scaling in gauge/string correspondence
• Hexagonalization of Correlation Functions
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Exponential suppression with four legs and an infinity of loops
• Combinatorial Solution of the Eclectic Spin Chain
• Spectrum of the Hypereclectic Spin Chain and Pólya Counting

Cited by in corpus (2)

• The Loom for General Fishnet CFTs
• Checkerboard CFT