TY - JOUR
T1 - Manifestly dual-conformal loop integration
AU - Bourjaily, Jacob L.
AU - Dulat, Falko
AU - Panzer, Erik
N1 - Funding Information:
This work began in collaboration with Lance Dixon and we are indebted to him for helping with many of the explicit results for the six particle amplitude. We are grateful to JJ Carrasco for helpful comments on early drafts of this work; to Andrew McLeod, Matt von Hippel, and Matthias Wilhelm for help with the integration of and its comparison with the results obtained by the hexagon bootstrap program; and to Nima Arkani-Hamed, Marcus Spradlin and Jaroslav Trnka for useful discussions. This work was supported in part by the Danish National Research Foundation ( DNRF91 ), a grant from the Villum Fonden , and a Starting Grant (No. 757978 ) from the European Research Council , and a grant from the Simons Foundation ( 341344 , LA) (JLB), as well as by the U.S. Department of Energy (DOE) under contract DE-AC02-76SF00515 (FD). Finally, the authors are grateful for the hospitality and support from the Institute for Advanced Study in Princeton, the Munich Institute for Astro- and Particle Physics (MIAPP), the Mainz Institute for Theoretical Physics (MITP), and the Galileo Galilei Institute in Florence .
Publisher Copyright:
© 2019 The Author(s)
PY - 2019/5
Y1 - 2019/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.nuclphysb.2019.03.022
DO - 10.1016/j.nuclphysb.2019.03.022
M3 - Article
AN - SCOPUS:85063939086
VL - 942
SP - 251
EP - 302
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
ER -