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1902
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2020

Positive Geometries for One-Loop Chiral Octagons

Herrmann, Enrico, Langer, Cameron, Trnka, Jaroslav et al.

Understand

Inspired by the topological sign-flip definition of the Amplituhedron, we introduce similar, but distinct, positive geometries relevant for one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory.

The simplest geometries are those with the maximal number of sign flips, and turn out to be associated with chiral octagons previously studied in the context of infrared (IR) finite, pure and dual conformal invariant local integrals.
Our result bridges two different themes of the modern amplitudes program: positive geometry and Feynman integrals.

Built on

C. Langer and A. Yelleshpur Srikant, JHEP 04
Original
1902
Earlier work this paper cites.
D. Damgaard, L. Ferro, T. Lukowski, and M. Parisi, JHEP 08
Original
1905
Earlier work this paper cites.
E. Herrmann and J. Parra-Martinez, JHEP 02
Original
1909
Earlier work this paper cites.
N. Arkani-Hamed, S. He, and T. Lam, (2019b), arXiv:1912.08707
Original
1912
Earlier work this paper cites.
G. ’t Hooft, Nucl. Phys. B 72
1974
Earlier work this paper cites.
L. Brink, J. H. Schwarz, and J. Scherk, Nucl.Phys. B121
1977
Earlier work this paper cites.
F. Gliozzi, J. Scherk, and D. I. Olive, Nucl.Phys. B122
1977
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Nucl.Phys. B425
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Nucl.Phys. B435
1995
Earlier work this paper cites.
S. He, L. Ren, and Y. Zhang, JHEP 04
Original
2001
Earlier work this paper cites.
R. Kojima and C. Langer, JHEP 05
Original
2001
Earlier work this paper cites.