Built on

D. Damgaard, L. Ferro, T. Lukowski, and M. Parisi, “The Momentum Amplituhedron,” JHEP
Original
1905
Earlier work this paper cites.
T. Łukowski, M. Parisi, M. Spradlin, and A. Volovich, “Cluster Adjacency for m = 2 m=2 Yangian Invariants,” JHEP
Original
1908
Earlier work this paper cites.
P. Benincasa, “Cosmological Polytopes and the Wavefuncton of the Universe for Light States,” arXiv:1909.02517 [hep-th]
Original
1909
Earlier work this paper cites.
G. E. Collins, “Quantifier elimination for real closed fields by cylindrical algebraic decomposition: A synopsis,” SIGSAM Bull
1976
Earlier work this paper cites.
P. Benincasa and M. Parisi, “Positive Geometries and Differential Forms with Non-Logarithmic Singularities I,” arXiv:2005.03612 [hep-th]
Original
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP
Original
2007
Earlier work this paper cites.
E. Herrmann, C. Langer, J. Trnka, and M. Zheng, “Positive geometry, local triangulations, and the dual of the Amplituhedron,” JHEP
Original
2009
Earlier work this paper cites.
J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, “Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory,” Nucl. Phys. B
Original
2010
Earlier work this paper cites.
L. F. Alday, B. Eden, G. P. Korchemsky, J. Maldacena, and E. Sokatchev, “From correlation functions to wilson loops,” Journal of High Energy Physics
2011
Earlier work this paper cites.
B. Eden, G. P. Korchemsky, and E. Sokatchev, “From correlation functions to scattering amplitudes,” Journal of High Energy Physics
2011
Earlier work this paper cites.
T. Adamo, M. Bullimore, L. Mason, and D. Skinner, “A proof of the correlation function/supersymmetric wilson loop correspondence,” Journal of High Energy Physics
2011
Earlier work this paper cites.

Similar

L. Mason and D. Skinner, “Amplitudes at Weak Coupling as Polytopes in AdS_5,” J. Phys. A
Original
2011
Cited alongside, same era.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges, and J. Trnka, “A Note on Polytopes for Scattering Amplitudes,” JHEP
Original
2012
Cited alongside, same era.
B. Eden, G. P. Korchemsky, and E. Sokatchev, “More on the duality correlators/amplitudes,” Physics Letters B
2012
Cited alongside, same era.
B. Eden, P. Heslop, G. P. Korchemsky, and E. Sokatchev, “The super-correlator/super-amplitude duality: Part i,” Nuclear Physics B
2012
Cited alongside, same era.
B. Eden, P. Heslop, G. P. Korchemsky, and E. Sokatchev, “The super-correlator/super-amplitude duality: Part ii,” Nuclear Physics B
2012
Cited alongside, same era.

Then

J. L. Bourjaily, P. Heslop, and V.-V. Tran, “Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N=4 Supersymmetric Yang-Mills Theory,” Phys. Rev. Lett
Original
2016
Later among the works it cites.
J. L. Bourjaily, P. Heslop, and V.-V. Tran, “Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps,” JHEP
Original
2016
Later among the works it cites.
Cambridge University Press, 4, 2016
Original
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov, and J. Trnka, Grassmannian Geometry of Scattering Amplitudes · 2016
Later among the works it cites.
N. Arkani-Hamed, Y. Bai and T. Lam, “Positive Geometries and Canonical Forms,” JHEP 11
Original
2017
Later among the works it cites.

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2021

Amplituhedron-like geometries

Dian, Gabriele, Heslop, Paul

Understand

We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number.

We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level.
The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of.
We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level.

Built on

D. Damgaard, L. Ferro, T. Lukowski, and M. Parisi, “The Momentum Amplituhedron,” JHEP
Original
1905
Earlier work this paper cites.
T. Łukowski, M. Parisi, M. Spradlin, and A. Volovich, “Cluster Adjacency for m = 2 m=2 Yangian Invariants,” JHEP
Original
1908
Earlier work this paper cites.
P. Benincasa, “Cosmological Polytopes and the Wavefuncton of the Universe for Light States,” arXiv:1909.02517 [hep-th]
Original
1909
Earlier work this paper cites.
G. E. Collins, “Quantifier elimination for real closed fields by cylindrical algebraic decomposition: A synopsis,” SIGSAM Bull
1976
Earlier work this paper cites.
P. Benincasa and M. Parisi, “Positive Geometries and Differential Forms with Non-Logarithmic Singularities I,” arXiv:2005.03612 [hep-th]
Original
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP
Original
2007
Earlier work this paper cites.
E. Herrmann, C. Langer, J. Trnka, and M. Zheng, “Positive geometry, local triangulations, and the dual of the Amplituhedron,” JHEP
Original
2009
Earlier work this paper cites.
J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, “Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory,” Nucl. Phys. B
Original
2010
Earlier work this paper cites.
L. F. Alday, B. Eden, G. P. Korchemsky, J. Maldacena, and E. Sokatchev, “From correlation functions to wilson loops,” Journal of High Energy Physics
2011
Earlier work this paper cites.
B. Eden, G. P. Korchemsky, and E. Sokatchev, “From correlation functions to scattering amplitudes,” Journal of High Energy Physics
2011
Earlier work this paper cites.
T. Adamo, M. Bullimore, L. Mason, and D. Skinner, “A proof of the correlation function/supersymmetric wilson loop correspondence,” Journal of High Energy Physics
2011
Earlier work this paper cites.

Similar

L. Mason and D. Skinner, “Amplitudes at Weak Coupling as Polytopes in AdS_5,” J. Phys. A
Original
2011
Cited alongside, same era.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges, and J. Trnka, “A Note on Polytopes for Scattering Amplitudes,” JHEP
Original
2012
Cited alongside, same era.
B. Eden, G. P. Korchemsky, and E. Sokatchev, “More on the duality correlators/amplitudes,” Physics Letters B
2012
Cited alongside, same era.
B. Eden, P. Heslop, G. P. Korchemsky, and E. Sokatchev, “The super-correlator/super-amplitude duality: Part i,” Nuclear Physics B
2012
Cited alongside, same era.
B. Eden, P. Heslop, G. P. Korchemsky, and E. Sokatchev, “The super-correlator/super-amplitude duality: Part ii,” Nuclear Physics B
2012
Cited alongside, same era.

Then

J. L. Bourjaily, P. Heslop, and V.-V. Tran, “Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N=4 Supersymmetric Yang-Mills Theory,” Phys. Rev. Lett
Original
2016
Later among the works it cites.
J. L. Bourjaily, P. Heslop, and V.-V. Tran, “Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps,” JHEP
Original
2016
Later among the works it cites.
Cambridge University Press, 4, 2016
Original
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov, and J. Trnka, Grassmannian Geometry of Scattering Amplitudes · 2016
Later among the works it cites.
N. Arkani-Hamed, Y. Bai and T. Lam, “Positive Geometries and Canonical Forms,” JHEP 11
Original
2017
Later among the works it cites.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

B. Eden, P. Heslop, G. P. Korchemsky, and E. Sokatchev, “Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM,” Nucl. Phys. B

Original

2012

Cited alongside, same era.

B. Eden, P. Heslop, G. P. Korchemsky, and E. Sokatchev, “Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM,” Nucl. Phys. B

Original

2012

Cited alongside, same era.

N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, and J. Trnka, “Local Integrals for Planar Scattering Amplitudes,” JHEP

Original

2012

Cited alongside, same era.

A. Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,” JHEP

Original

2013

Cited alongside, same era.

A. Hodges, “The Box Integrals in Momentum-Twistor Geometry,” JHEP

Original

2013

Cited alongside, same era.

D. Chicherin, R. Doobary, B. Eden, P. Heslop, G. P. Korchemsky, L. Mason, and E. Sokatchev, “Correlation functions of the chiral stress-tensor multiplet in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP

Original

2015

Cited alongside, same era.

D. Damgaard, L. Ferro, T. Lukowski, and R. Moerman, “Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry,” arXiv:2103.13908 [hep-th]

Original

Cited in the paper.

B. Eden, P. Heslop, and L. Mason, “The correlahedron,” Journal of High Energy Physics

2017