Twistor fishnets

TL;DR

This paper reformulates four-dimensional conformal fishnet theory within twistor space, providing new cohomological methods for calculating scattering amplitudes that highlight its conformal symmetry.

Contribution

It introduces a twistor space reformulation of the conformal fishnet theory derived from gamma-deformed super-Yang-Mills, enabling novel amplitude computations.

Findings

Cohomological formulae for scattering amplitudes

Manifestation of conformal invariance in twistor space

Retention of abelian gauge symmetry on twistor space

Abstract

Four-dimensional conformal fishnet theory is an integrable scalar theory which arises as a double scaling limit of $\gamma$-deformed maximally supersymmetric Yang-Mills. We give a perturbative reformulation of $\gamma$-deformed super-Yang-Mills theory in twistor space, and implement the double scaling limit to obtain a twistor description of conformal fishnet theory. The conformal fishnet theory retains an abelian gauge symmetry on twistor space which is absent in space-time, allowing us to obtain cohomological formulae for scattering amplitudes that manifest conformal invariance. We study various classes of scattering amplitudes in twistor space with this formalism.