We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. 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 non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell 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 one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.
Cheung, Clifford, et al. "A periodic table of effective field theories." Journal of High Energy Physics (Online), vol. 2017, no. 2, Feb. 2017. https://doi.org/10.1007/JHEP02(2017)020
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, Shen, Chia -Hsien, & Trnka, Jaroslav (2017). A periodic table of effective field theories. Journal of High Energy Physics (Online), 2017(2). https://doi.org/10.1007/JHEP02(2017)020
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, et al., "A periodic table of effective field theories," Journal of High Energy Physics (Online) 2017, no. 2 (2017), https://doi.org/10.1007/JHEP02(2017)020
@article{osti_1356089,
author = {Cheung, Clifford and Kampf, Karol and Novotny, Jiri and Shen, Chia -Hsien and Trnka, Jaroslav},
title = {A periodic table of effective field theories},
annote = {We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. 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 non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell 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 one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.},
doi = {10.1007/JHEP02(2017)020},
url = {https://www.osti.gov/biblio/1356089},
journal = {Journal of High Energy Physics (Online)},
issn = {ISSN 1029-8479},
number = {2},
volume = {2017},
place = {United States},
publisher = {Springer Berlin},
year = {2017},
month = {02}}
Bondi, Hermann; Van der Burg, M. G. J.; Metzner, A. W. K.
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 269, Issue 1336, p. 21-52https://doi.org/10.1098/rspa.1962.0161
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 270, Issue 1340, p. 103-126https://doi.org/10.1098/rspa.1962.0206