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Published February 2017 | Submitted + Published
Journal Article Open

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 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. 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.

Additional Information

© 2017 The Author(s). 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: November 27, 2016; Revised: January 25, 2017; Accepted: January 26, 2017; Published: February 6, 2017. We thank Nima Arkani-Hamed and Enrico Herrmann for discussions. We also thank Tom Melia for pointing out a typo in the earlier version. This work is supported in part by Czech Government project no. LH14035 and GACR 15-18080S. C.C. and C.-H.S. are supported by a Sloan Research Fellowship and a DOE Early Career Award under grant no. DESC0010255. C.-H.S. thanks Nordita and Niels Bohr International Academy and Discovery Center for hospitality.

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Published - art_3A10.1007_2FJHEP02_282017_29020.pdf

Submitted - 1611.03137v1.pdf


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