# Yangian Symmetry for Bi-Scalar Loop Amplitudes

## TL;DR

This paper proves an all-loop conformal Yangian symmetry for planar amplitudes in a bi-scalar field theory, revealing integrability and explicit symmetry generators, and relates it to dual conformal symmetry.

## Contribution

It establishes the all-loop Yangian symmetry for bi-scalar amplitudes and explicitly constructs the level-one generators, advancing understanding of integrability in this theory.

## Key findings

- Yangian symmetry holds at all loops for bi-scalar amplitudes.
- Explicit construction of level-one Yangian generators.
- Connection between Yangian symmetry and dual conformal symmetry.

## Abstract

We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of gamma-twisted weakly coupled N=4 SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.