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 (a.k.a. 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.
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Acknowledgments
It is a pleasure to thank Kevin Costello for useful conversations. This research was supported in part by a grant from the Krembil Foundation. DG is supported by the NSERC Discovery Grant program and by the Perimeter Institute for Theoretical Physics. JK is funded through the NSERC CGS-D program. JW is supported by the European Union’s Horizon 2020 Framework: ERC grant 682608 and the “Simons collaboration on Special Holonomy in Geometry, Analysis and Physics”. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
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Budzik, K., Gaiotto, D., Kulp, J. et al. Feynman diagrams in four-dimensional holomorphic theories and the Operatope. J. High Energ. Phys. 2023, 127 (2023). https://doi.org/10.1007/JHEP07(2023)127
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DOI: https://doi.org/10.1007/JHEP07(2023)127