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Massive Conformal Symmetry and Integrability for Feynman Integrals.

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Integrability is found in massive quantum field theories, extending dual conformal symmetry. This discovery introduces a massive momentum space conformal symmetry, applicable to Feynman integrals and suggesting AdS/CFT interpretations.

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Area of Science:

  • Quantum Field Theory
  • High Energy Physics
  • Mathematical Physics

Background:

  • Integrability is crucial for solving massless quantum field theories like N=4 super Yang-Mills theory.
  • Previous work identified massive dual conformal symmetry in N=4 super Yang-Mills theory on the Coulomb branch.

Purpose of the Study:

  • To investigate the role of integrability in massive quantum field theories.
  • To prove the existence of massive Yangian symmetry in massive Feynman integrals.
  • To introduce and explore a massive generalization of momentum space conformal symmetry.

Main Methods:

  • Proving invariance of massive n-gon Feynman integrals under massive Yangian symmetry at one-loop order.
  • Extending proofs to two-loop graphs and conjecturing invariance for higher-loop graphs from planar tilings.
  • Translating Yangian generators to introduce massive momentum space conformal symmetry.

Main Results:

  • All massive n-gon Feynman integrals in generic spacetime dimensions exhibit massive Yangian symmetry at one-loop.
  • A novel massive momentum space conformal symmetry is introduced, generalizing conformal symmetry to massive integrals.
  • The Yangian unifies massive dual conformal symmetry and the new massive momentum space conformal symmetry.

Conclusions:

  • Integrability is a fundamental feature of massive quantum field theories, not just massless ones.
  • The discovered Yangian symmetry and its extensions offer new tools for analyzing Feynman integrals.
  • Findings suggest potential interpretations via AdS/CFT correspondence and applications in bootstrapping Feynman integral building blocks.