Feynman Diagrams in Four-Dimensional Holomorphic Theories and the Operatope

Abstract

We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (aka the ``Operatope''). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories.

arXiv comment45 pages, Mathematica code attached

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• Gauging The Diamond: Integrable Coset Models from Twistor Space
• Combinatorial proof of a Non-Renormalization Theorem
• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
• Holomorphic field theories and higher algebra
• Loop Corrected Supercharges from Holomorphic Anomalies