Manifestly dual-conformal loop integration

Bourjaily, Jacob L. (Niels Bohr International Academy, Discovery Center, University of Copenhagen, The Niels Bohr Institute, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark) ; Dulat, Falko (SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94309, USA) ; Panzer, Erik (All Souls College, University of Oxford, Oxford, OX1 4AL, UK)

09 April 2019

Abstract: Local, manifestly dual-conformally invariant loop integrands are now known for all finite quantities associated with observables in planar, maximally supersymmetric Yang-Mills theory through three loops. These representations, however, are not infrared-finite term by term and therefore require regularization; and even using a regulator consistent with dual-conformal invariance, ordinary methods of loop integration would naïvely obscure this symmetry. In this work, we show how any planar loop integral through at least two loops can be systematically regulated and evaluated directly in terms of strictly finite, manifestly dual-conformal Feynman-parameter integrals. We apply these methods to the case of the two-loop ratio and remainder functions for six particles, reproducing the known results in terms of individually regulated local loop integrals, and we comment on some of the novelties that arise for this regularization scheme not previously seen at one loop.

Published in: Nuclear Physics B 942 (2019) 251-302 DOI: 10.1016/j.nuclphysb.2019.03.022
License: CC-BY-3.0

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