Fetching the paper…

Reading the bibliography…

2019

Accordiohedra as positive geometries for generic scalar field theories

Aneesh, P. B., Jagadale, Mrunmay, Kalyanapuram, Nikhil

Original
PDF
Post on X

Understand

We build upon the prior works of [1-3] to study tree-level planar amplitudes for a massless scalar field theory with polynomial interactions.

Focusing on a specific example, where the interaction is given by $\lambda_3\phi^{3}\ +\lambda_4 \phi^{4}$, we show that a specific convex realization of a simple polytope known as the accordiohedron in kinematic space is the positive geometry for this theory.
As in the previous cases, there is a unique planar scattering form in kinematic space, associated to each positive geometry which yields planar scattering amplitudes.

Accordiohedra as positive geometries for generic scalar field theories · Around

Built on

P. Raman, “The positive geometry for ϕ p \phi^{p} interactions,” arXiv:1906.02985 [hep-th]
Original
1906
Earlier work this paper cites.
A. Padrol, Y. Palu, V. Pilaud, and P.-G. Plamondon, “Associahedra for finite type cluster algebras and minimal relations between 𝐠 \mathbf{g} -vectors,” arXiv:1906.06861 [math.RT]
Original
1906
Earlier work this paper cites.
P. B. Aneesh, P. Banerjee, M. Jagadale, R. Rajan, A. Laddha, and S. Mahato, “On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms,” arXiv:1911.06008 [hep-th]
Original
1911
Earlier work this paper cites.
Springer, 2001
Y. Baryshnikov, “On stokes sets,” in New developments in singularity theory · 2001
Earlier work this paper cites.
J.-L. Loday, “Realization of the stasheff polytope,” Archiv der Mathematik
2004
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP
Original
2007
Earlier work this paper cites.

Similar

N. Arkani-Hamed and J. Trnka, “Into the Amplituhedron,” JHEP
Original
2014
Cited alongside, same era.
F. Cachazo, S. He, and E. Y. Yuan, “Scattering of Massless Particles: Scalars, Gluons and Gravitons,” JHEP
Original
2014
Cited alongside, same era.
N. Arkani-Hamed, A. Hodges, and J. Trnka, “Positive Amplitudes In The Amplituhedron,” JHEP
Original
2015
Cited alongside, same era.
C. Ceballos, F. Santos, and G. M. Ziegler, “Many non-equivalent realizations of the associahedron,” Combinatorica
Original
2015
Cited alongside, same era.
X. Gao, S. He, and Y. Zhang, “Labelled tree graphs, Feynman diagrams and disk integrals,” JHEP
Original

Then

N. Arkani-Hamed, Y. Bai, S. He, and G. Yan, “Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet,” JHEP
Original
2018
Later among the works it cites.
N. Arkani-Hamed, H. Thomas, and J. Trnka, “Unwinding the Amplituhedron in Binary,” JHEP
Original
2018
Later among the works it cites.
N. Arkani-Hamed, C. Langer, A. Yelleshpur Srikant, and J. Trnka, “Deep Into the Amplituhedron: Amplitude Singularities at All Loops and Legs,” Phys. Rev. Lett
Original
2019
Closest in time.
T. Manneville and V. Pilaud, “Geometric realizations of the accordion complex of a dissection,” Discrete & Computational Geometry
Original
2019
Closest in time.
S. He and Q. Yang, “An Etude on Recursion Relations and Triangulations,” JHEP

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2017

Cited alongside, same era.

N. Arkani-Hamed, Y. Bai, and T. Lam, “Positive Geometries and Canonical Forms,” JHEP

2017

Cited alongside, same era.

P. Banerjee, A. Laddha, and P. Raman, “Stokes Polytopes : The positive geometry for ϕ 4 \phi^{4} interactions,” arXiv:1811.05904 [hep-th]

Cited in the paper.

F. Chapoton, “Stokes posets and serpent nests,” arXiv:1505.05990 [math.RT]

Cited in the paper.

G. Salvatori, “1-loop Amplitudes from the Halohedron,” arXiv:1806.01842 [hep-th]

Cited in the paper.

2019

Closest in time.