Abstract
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as super Yang-Mills theory. In this Letter, we show that integrability also features in the building blocks of massive quantum field theories. At one-loop order we prove that all massive -gon Feynman integrals in generic spacetime dimensions are invariant under a massive Yangian symmetry. At two loops similar statements can be proven for graphs built from two -gons. At generic loop order we conjecture that all graphs cut from regular tilings of the plane with massive propagators on the boundary are invariant. We support this conjecture by a number of numerical tests for higher loops and legs. The observed Yangian extends the bosonic part of the massive dual conformal symmetry that was found a decade ago on the Coulomb branch of super Yang-Mills theory. By translating the Yangian level-one generators from dual to original momentum space, we introduce a massive generalization of momentum space conformal symmetry. Even for non-dual-conformal integrals this novel symmetry persists. The Yangian can thus be understood as the closure of massive dual conformal symmetry and this new massive momentum space conformal symmetry, which suggests an interpretation via . As an application of our findings, we bootstrap the hypergeometric building blocks for examples of massive Feynman integrals.
- Received 22 May 2020
- Accepted 22 July 2020
DOI:https://doi.org/10.1103/PhysRevLett.125.091602
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society