Exact scattering amplitudes in conformal fishnet theory

Abstract

We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of $\gamma$-deformed $\mathcal{N}=4$ SYM. We show that the single-trace partial amplitude is protected from quantum corrections whereas the double-trace partial amplitude is a nontrivial infrared finite function of the ratio of Mandelstam invariants. Applying the Lehmann--Symanzik--Zimmerman reduction procedure to the known expression of a four-point correlation function in the fishnet theory, we derive a new representation for this function that is valid for arbitrary coupling. We use this representation to find the asymptotic behavior of the double-trace amplitude in the high-energy limit and to compute the corresponding exact Regge trajectories. We verify that at weak coupling the expressions obtained are in agreement with an explicit five-loop calculation.

arXiv comment31 pages, 3 figures

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• The Loom for General Fishnet CFTs
• Conformal Regge Theory at Finite Boost
• A Collinear Perspective on the Regge Limit
• Twistor fishnets
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
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