Yangian Symmetry Escapes from the Fishnet

TL;DR

This paper explores the classical Yangian symmetry in four-dimensional fishnet models, revealing its limitations at the quantum level and its dependence on specific evaluation parameters.

Contribution

It demonstrates that Yangian symmetry is classically realized in these models but does not extend to generic quantum correlation functions, highlighting obstacles to quantum integrability.

Findings

Yangian symmetry is classically realized with specific evaluation parameters.

Quantum correlation functions generally lack Yangian invariance.

Non-zero dual Coxeter number hinders quantum Yangian symmetry.

Abstract

We investigate Yangian symmetry for the equations of motion and the action of the classical bi-scalar and supersymmetric fishnet models in four spacetime dimensions, and we subsequently discuss its applicability to planar correlation functions. We argue that Yangian symmetry is classically realised in these models subject to specific evaluation parameter patterns. Curiously, Yangian invariance does not extend to generic quantum correlation functions in the bi-scalar model beyond the well-established classes of Yangian invariant correlators. We present several concrete counter-examples of bi-scalar correlators given by sums of Feynman graphs and of bi-scalar graphs with octagon-shaped loops. This finding underlines the notion that a non-zero dual Coxeter number represents an obstacle towards quantum Yangian symmetry and possibly also for complete integrability in planar QFT models.