Fetching the paper…

Reading the bibliography…

2014

Positive Amplitudes In The Amplituhedron

Arkani-Hamed, Nima, Hodges, Andrew, Trnka, Jaroslav

Original
PDF
Post on X

Understand

The all-loop integrand for scattering amplitudes in planar N = 4 SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron.

In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron.
The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry.
However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian.

Positive Amplitudes In The Amplituhedron · Around

Built on

R. Britto, F. Cachazo, B. Feng and E. Witten, Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, Nucl. Phys. B 715
2005
Earlier work this paper cites.
Z. Bern, L. J. Dixon and V. A. Smirnov, Phys. Rev. D 72
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, JHEP 1410
Original
2007
Earlier work this paper cites.
Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower and V. A. Smirnov, Phys. Rev. D 75
2007
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco, H. Johansson and D. A. Kosower, Phys. Rev. D 76
Original
2007
Earlier work this paper cites.

Similar

M. Bullimore, L. J. Mason and D. Skinner, “MHV Diagrams in Momentum Twistor Space,” JHEP 1012
Original
2010
Cited alongside, same era.
H. Elvang, D. Z. Freedman and M. Kiermaier, JHEP 1003
Original
2010
Cited alongside, same era.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, JHEP 1101
Original
2011
Cited alongside, same era.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges and J. Trnka, JHEP 1204
Original
2012
Cited alongside, same era.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo and J. Trnka, JHEP 1206
Original
2012

Then

B. Eden, P. Heslop, G. P. Korchemsky and E. Sokatchev, Nucl. Phys. B 862
Original
2012
Later among the works it cites.
L. J. Dixon, J. M. Drummond and J. M. Henn, JHEP 1201
Original
2012
Later among the works it cites.
A. Hodges, JHEP 1305
Original
2013
Later among the works it cites.
Z. Bern, J. J. Carrasco, L. J. Dixon, M. R. Douglas, M. von Hippel and H. Johansson, Phys. Rev. D 87
Original
2013
Later among the works it cites.
L. J. Dixon and M. von Hippel, JHEP 1410
Original
2014
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

J. L. Bourjaily, A. DiRe, A. Shaikh, M. Spradlin and A. Volovich, JHEP 1203

2012

Cited alongside, same era.

N. Arkani-Hamed and J. Trnka, arXiv:1312.7878 [hep-th]

Cited in the paper.

S. Franco, D. Galloni, A. Mariotti and J. Trnka, arXiv:1408.3410 [hep-th]

Cited in the paper.

Y. Bai and S. He, arXiv:1408.2459 [hep-th]

Cited in the paper.

T. Lam, arXiv:1408.5531 [math.AG]

Original

Cited in the paper.

N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, arXiv:1212.5605 [hep-th]

Cited in the paper.

J. L. Bourjaily, arXiv:1011.2447 [hep-ph]

Cited in the paper.