Exact scattering amplitudes in conformal fishnet theory

  • G. P. KorchemskyEmail author
Open Access
Regular Article - Theoretical Physics


We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of γ-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.


Scattering Amplitudes Conformal Field Theory Integrable Field Theories 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Institut de Physique Théorique, (Unité Mixte de Recherche 3681 du CNRS) Université Paris Saclay, CNRS, CEAGif-sur-YvetteFrance

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