TY - JOUR

T1 - Massive Conformal Symmetry and Integrability for Feynman Integrals

AU - Loebbert, Florian

AU - Miczajka, Julian

AU - Mueller, Dennis

AU - Muenkler, Hagen

PY - 2020/8/25

Y1 - 2020/8/25

N2 - In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N = 4 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 n-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 n-gons. At generic loop order we conjecture that all graphs cut from regular Wings 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 N = 4 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 AdS/CFT. As an application of our findings, we bootstrap the hypergeometric building blocks for examples of massive Feynman integrals.

AB - In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N = 4 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 n-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 n-gons. At generic loop order we conjecture that all graphs cut from regular Wings 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 N = 4 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 AdS/CFT. As an application of our findings, we bootstrap the hypergeometric building blocks for examples of massive Feynman integrals.

U2 - 10.1103/PhysRevLett.125.091602

DO - 10.1103/PhysRevLett.125.091602

M3 - Journal article

C2 - 32915614

VL - 125

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 9

M1 - 091602

ER -