The EFT-hedron
Abstract
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 "EFT-hedron". We initiate a systematic investigation of the boundary structure of the EFT-hedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFT-hedron 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.
Additional Information
© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: April 11, 2021; Accepted: April 19, 2021; Published: May 27, 2021. We thank Alex Postnikov, Steven Karp and Congkao Wen for stimulating discussions. We thank Zvi Bern, Alexander Zhiboedov, and Dimitrios Kosmopoulos for discussions, and for pointing out an error in the spinning residue polynomials given in the first version of the paper. N.A-H. is supported by DOE grant de-sc0009988. Y-t H is supported by MoST Grant No. 106-2628-M-002-012-MY3. T-c H is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DESC0011632.Attached Files
Published - Arkani-Hamed2021_Article_TheEFT-hedron.pdf
Submitted - 2012.15849.pdf
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Additional details
- Eprint ID
- 107377
- Resolver ID
- CaltechAUTHORS:20210107-151727295
- DE-SC0009988
- Department of Energy (DOE)
- 106-2628-M-002-012-MY3
- Ministry of Science and Technology (Taipei)
- DE-SC0011632
- Department of Energy (DOE)
- SCOAP3
- Created
-
2021-01-08Created from EPrint's datestamp field
- Updated
-
2021-05-27Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2020-061