A periodic table of effective field theories
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local Smatrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the nonlinear sigma model, DiracBornInfeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using onshell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Finally, our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are oneparameter theories whose interactions are strictly dictated by properties of the Smatrix.
 Authors:

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 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Charles Univ., Prague (Czech Republic)
 Univ. of California, Davis, CA (United States)
 Publication Date:
 Grant/Contract Number:
 SC0010255
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; gaugetheory; gravitational waves; general relativity; tree amplitudes; currentalgebra; space
 OSTI Identifier:
 1356089
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, Shen, Chia Hsien, and Trnka, Jaroslav. A periodic table of effective field theories. United States: N. p.,
Web. doi:10.1007/JHEP02(2017)020.
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, Shen, Chia Hsien, & Trnka, Jaroslav. A periodic table of effective field theories. United States. doi:10.1007/JHEP02(2017)020.
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, Shen, Chia Hsien, and Trnka, Jaroslav. 2017.
"A periodic table of effective field theories". United States.
doi:10.1007/JHEP02(2017)020. https://www.osti.gov/servlets/purl/1356089.
@article{osti_1356089,
title = {A periodic table of effective field theories},
author = {Cheung, Clifford and Kampf, Karol and Novotny, Jiri and Shen, Chia Hsien and Trnka, Jaroslav},
abstractNote = {We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local Smatrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the nonlinear sigma model, DiracBornInfeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using onshell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Finally, our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are oneparameter theories whose interactions are strictly dictated by properties of the Smatrix.},
doi = {10.1007/JHEP02(2017)020},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2017,
place = {United States},
year = {2017},
month = {2}
}