Massive Conformal Symmetry and Integrability for Feynman Integrals

Abstract

In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM 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 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 N=4 SYM 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.

arXiv comment6 pages, v2: typos corrected, clarifications added, v3: minor improvements/corrections, title adapted to journal title, v4: signs in (11) and (23) and prefactors in (22) and footnote [20] corrected

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Cited by in corpus (20)

• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Yangian Bootstrap for Massive Feynman Integrals
• The Wilson-loop $d\log$ representation for Feynman integrals
• Massive Fishnets
• Massive One-loop Conformal Feynman Integrals and Quadratic Transformations of Multiple Hypergeometric Series
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Integrability for Feynman Integrals
• Cosmic Wheels: From integrability to the Galois coaction
• Minkowski Box from Yangian Bootstrap
• Yangian Symmetry in Holographic Correlators
• Shift operators from the simplex representation in momentum-space CFT
• 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
• The Conformal Anomaly Action to Fourth Order (4T) in $d=4$ in Momentum Space