Abstract
We derive a variant of the loop-tree duality for Feynman integrals in the Schwinger parametric representation. This is achieved by decomposing the integration domain into a disjoint union of cells, one for each spanning tree of the graph under consideration. Each of these cells is the total space of a fiber bundle with contractible fibers over a cube. Loop-tree duality emerges then as the result of first decomposing the integration domain, then integrating along the fibers of each fiber bundle.
As a byproduct we obtain a new proof that the moduli space of graphs is homotopy equivalent to its spine. In addition, we outline a potential application to Kontsevich’s graph (co-)homology.
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ArXiv ePrint: 2208.07636
Für Niels Andersen, anstelle der Sonnenuhr.
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Berghoff, M. Schwinger, ltd: loop-tree duality in the parametric representation. J. High Energ. Phys. 2022, 178 (2022). https://doi.org/10.1007/JHEP10(2022)178
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DOI: https://doi.org/10.1007/JHEP10(2022)178