Massive Fishnets

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 Gürdoğan 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.

32 pages, v2: figure 1 and sign in eq (3.3) corrected, v3: minor improvements, signs in (3.6),(3.19) and (C.1) corrected

References in corpus (9)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Exacting N=4 Superconformal Symmetry
• Large N Field Theory and AdS Tachyons
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Lectures on Yangian Symmetry
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• Yangians, S-matrices and AdS/CFT
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Chaos in the Fishnet

Cited by in corpus (10)

• Feynman Polytopes and the Tropical Geometry of UV and IR Divergences
• Yangian Bootstrap for Massive Feynman Integrals
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Integrability for Feynman Integrals
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• The Feyn-Structure of Yangian Symmetry
• Non-Local Symmetries of Planar Feynman Integrals
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions