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Abstract: We investigate relations between loop and tree amplitudes in quantum fieldtheory that involve putting on-shell some loop propagators. This generalizesthe so-called Feynman tree theorem which is satisfied at 1-loop. Exploitingretarded boundary conditions, we give a generalization to L-loop expressing theloops as integrals over the on-shell phase space of exactly L particles. Weargue that the corresponding integrand for L>2 does not involve the forwardlimit of any physical tree amplitude, except in planar gauge theories. In thatcase we explicitly construct the relevant physical amplitude. Beyond the planarlimit, abandoning direct integral representations, we propose that loopscontinue to be determined implicitly by the forward limit of physical connectedtrees, and we formulate a precise conjecture along this line. Finally, we setup technology to compute forward amplitudes in supersymmetric theories, inwhich specific simplifications occur.

Author: Simon Caron-Huot

Source: https://arxiv.org/

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