Massive Fishnets

TL;DR

This paper explores the integrability of massive Feynman integrals by connecting them to a massive fishnet theory derived from N=4 SYM, revealing Yangian symmetry and soft theorems in broken phases.

Contribution

It introduces a massive extension of the fishnet theory via Coulomb branch limits and links it to Yangian invariance of certain Feynman integrals, suggesting new avenues for integrability studies.

Findings

Massive Feynman integrals exhibit Yangian symmetry.

Planar off-shell amplitudes correspond to massive fishnet integrals.

Spontaneous symmetry breaking leads to soft theorems for scattering amplitudes.

Abstract

Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as correlators in the massless fishnet theory introduced by G\"urdo\u{g}an and Kazakov. Here we seek for an analogous interpretation of the integrability of massive Feynman integrals. We contrast two approaches to define simple massive quantum field theories in four dimensions. First, we discuss spontaneous symmetry breaking in the massless bi-scalar fishnet theory. We then propose an alternative route to a massive fishnet theory by taking a double-scaling limit of N=4 SYM theory on the Coulomb branch. Both approaches lead to a massive extension of the massless fishnet theory, differing in how masses enter into the propagators. In the latter theory, planar off-shell amplitudes are in one-to-one correspondence with precisely those massive Feynman integrals that were shown to be invariant under the Yangian. This suggests a re-investigation of Coulomb branch N=4 SYM theory with regard to integrability. Finally, we demonstrate that in the case of spontaneous symmetry breaking, the original conformal symmetry leads to soft theorems for scattering amplitudes in the broken phase.