Built on

M. B. Green and C. Wen, “Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values,” JHEP 1911
Original
1908
Earlier work this paper cites.
Hausdorff, F. "Summationsmethoden und Momentfolgen. I." Mathematische Zeitschrift 9, 74–109, 1921 Hausdorff, F. "Summationsmethoden und Momentfolgen. II." Mathematische Zeitschrift 9, 280–299, 1921
1921
Earlier work this paper cites.
W. Heisenberg, “Production of Meson Showers,” Nature 164
1949
Earlier work this paper cites.
Karlin, Samuel; McGregor, James. Coincidence properties of birth and death processes. Pacific J. Math. 9 (1959), no. 4, 1109–1140. https://projecteuclid.org/euclid.pjm/1103038888
1959
Earlier work this paper cites.
M. Froissart, “Asymptotic behavior and subtractions in the Mandelstam representation,” Phys. Rev. 123
1961
Earlier work this paper cites.
A. Martin, “Unitarity and high-energy behavior of scattering amplitudes,” Phys. Rev. 129
1963
Earlier work this paper cites.
A. Martin, “Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1.,” Nuovo Cim. A 42
1965
Earlier work this paper cites.
Y. Aharonov, A. Komar and L. Susskind, “Superluminal behavior, causality, and instability,” Phys. Rev. 182
1969
Earlier work this paper cites.

Similar

T. N. Pham and T. N. Truong, “Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation,” Phys. Rev. D 31
1985
Cited alongside, same era.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,” JHEP 0610
2006
Cited alongside, same era.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP 1410
Original
2007
Cited alongside, same era.
Y. t. Huang, J. Y. Liu, L. Rodina and Y. Wang, “Carving out the Space of Open-String S-matrix,” [arXiv:2008.02293 [hep-th]]
Original
2008
Cited alongside, same era.
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, “Positive Moments for Scattering Amplitudes,” [arXiv:2011.00037 [hep-th]]
Original

Then

B. Bellazzini, “Softness and amplitudes’ positivity for spinning particles,” JHEP 02
Original
2012
Later among the works it cites.
H. Elvang, D. Z. Freedman, L. Y. Hung, M. Kiermaier, R. C. Myers and S. Theisen, “On renormalization group flows and the a-theorem in 6d,” JHEP 1210
Original
2012
Later among the works it cites.
N. Arkani-Hamed, M. Pate, A. M. Raclariu and A. Strominger, “Celestial Amplitudes from UV to IR,” [arXiv:2012.04208 [hep-th]]
Original
2012
Later among the works it cites.
R. H. Boels and T. Hansen, “String theory in target space,” JHEP 06
Original
2014
Later among the works it cites.
X. O. Camanho, J. D. Edelstein, J. Maldacena and A. Zhiboedov, “Causality Constraints on Corrections to the Graviton Three-Point Coupling,” JHEP 1602

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2020

The EFT-Hedron

Arkani-Hamed, Nima, Huang, Tzu-Chen, Huang, Yu-tin

Understand

We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden "totally positive" structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra.

This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the "EFThedron".
We initiate a systematic investigation of the boundary structure of the EFThedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory.
We illustrate the EFThedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.

Built on

M. B. Green and C. Wen, “Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values,” JHEP 1911
Original
1908
Earlier work this paper cites.
Hausdorff, F. "Summationsmethoden und Momentfolgen. I." Mathematische Zeitschrift 9, 74–109, 1921 Hausdorff, F. "Summationsmethoden und Momentfolgen. II." Mathematische Zeitschrift 9, 280–299, 1921
1921
Earlier work this paper cites.
W. Heisenberg, “Production of Meson Showers,” Nature 164
1949
Earlier work this paper cites.
Karlin, Samuel; McGregor, James. Coincidence properties of birth and death processes. Pacific J. Math. 9 (1959), no. 4, 1109–1140. https://projecteuclid.org/euclid.pjm/1103038888
1959
Earlier work this paper cites.
M. Froissart, “Asymptotic behavior and subtractions in the Mandelstam representation,” Phys. Rev. 123
1961
Earlier work this paper cites.
A. Martin, “Unitarity and high-energy behavior of scattering amplitudes,” Phys. Rev. 129
1963
Earlier work this paper cites.
A. Martin, “Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1.,” Nuovo Cim. A 42
1965
Earlier work this paper cites.
Y. Aharonov, A. Komar and L. Susskind, “Superluminal behavior, causality, and instability,” Phys. Rev. 182
1969
Earlier work this paper cites.

Similar

T. N. Pham and T. N. Truong, “Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation,” Phys. Rev. D 31
1985
Cited alongside, same era.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,” JHEP 0610
2006
Cited alongside, same era.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP 1410
Original
2007
Cited alongside, same era.
Y. t. Huang, J. Y. Liu, L. Rodina and Y. Wang, “Carving out the Space of Open-String S-matrix,” [arXiv:2008.02293 [hep-th]]
Original
2008
Cited alongside, same era.
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, “Positive Moments for Scattering Amplitudes,” [arXiv:2011.00037 [hep-th]]
Original

Then

B. Bellazzini, “Softness and amplitudes’ positivity for spinning particles,” JHEP 02
Original
2012
Later among the works it cites.
H. Elvang, D. Z. Freedman, L. Y. Hung, M. Kiermaier, R. C. Myers and S. Theisen, “On renormalization group flows and the a-theorem in 6d,” JHEP 1210
Original
2012
Later among the works it cites.
N. Arkani-Hamed, M. Pate, A. M. Raclariu and A. Strominger, “Celestial Amplitudes from UV to IR,” [arXiv:2012.04208 [hep-th]]
Original
2012
Later among the works it cites.
R. H. Boels and T. Hansen, “String theory in target space,” JHEP 06
Original
2014
Later among the works it cites.
X. O. Camanho, J. D. Edelstein, J. Maldacena and A. Zhiboedov, “Causality Constraints on Corrections to the Graviton Three-Point Coupling,” JHEP 1602

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2011

Cited alongside, same era.

A. J. Tolley, Z. Y. Wang and S. Y. Zhou, “New positivity bounds from full crossing symmetry,” [arXiv:2011.02400 [hep-th]]

Original

2011

Cited alongside, same era.

S. Caron-Huot and V. Van Duong, “Extremal Effective Field Theories,” [arXiv:2011.02957 [hep-th]]

Original

2011

Cited alongside, same era.

A. Nicolis, R. Rattazzi and E. Trincherini, “Energy’s and amplitudes’ positivity,” JHEP 1005

Original

2011

Cited alongside, same era.

N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, “Grassmannian Geometry of Scattering Amplitudes,” doi:10.1017/CBO9781316091548 [arXiv:1212.5605 [hep-th]]

Original

Cited in the paper.

A. I. Davydychev, “Standard and hypergeometric representations for loop diagrams and the photon-photon scattering,” hep-ph/9307323

Cited in the paper.

N. Arkani-Hamed, T. C. Huang and Y. t. Huang, “Scattering Amplitudes For All Masses and Spins,” arXiv:1709.04891 [hep-th]

Original

Cited in the paper.

"Orbitopes" R. Sanyal, F. Sottile, B. Sturmfels, [arXiv:0911.5436 [hep-th]]

Original

Cited in the paper.

Original

2016

Later among the works it cites.

B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, “Beyond Positivity Bounds and the Fate of Massive Gravity,” Phys. Rev. Lett. 120

Original

2018

Later among the works it cites.

N. Arkani-Hamed, Y. T. Huang and S. H. Shao, “On the Positive Geometry of Conformal Field Theory,” JHEP 06

Original

2019

Later among the works it cites.

N. Arkani-Hamed and Y.-T. Huang, talk at Strings 2018; Lectures at the cern winter school on supergravity, strings and gauge theory (2019); talk at UV Meets the IR: Effective Field Theory Bounds from QFT to String Theory KITP 2020

2020

Closest in time.