A periodic table of effective field theories

Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia -Hsien; Trnka, Jaroslav

doi:10.1007/JHEP02(2017)020

Title: A periodic table of effective field theories

Journal Article · Mon Feb 06 00:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP02(2017)020· OSTI ID:1356089

Cheung, Clifford ^[1]; Kampf, Karol ^[2]; Novotny, Jiri ^[2]; Shen, Chia -Hsien ^[1]; Trnka, Jaroslav ^[3]

California Inst. of Technology (CalTech), Pasadena, CA (United States)
Charles Univ., Prague (Czech Republic)
Univ. of California, Davis, CA (United States)

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.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0010255

OSTI ID:: 1356089

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 2; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 115 works

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Double-soft behavior for scalars and gluons from string theory Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin arXiv https://doi.org/10.48550/arxiv.1507.00938	text	January 2015
Magnetic Corrections to the Soft Photon Theorem Strominger, Andrew arXiv https://doi.org/10.48550/arxiv.1509.00543	text	January 2015
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Aspects of Galileon Non-Renormalization Goon, Garrett; Hinterbichler, Kurt; Joyce, Austin arXiv https://doi.org/10.48550/arxiv.1606.02295	text	January 2016
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
gauge-theory
gravitational waves
general relativity
tree amplitudes
current-algebra
space

Title: A periodic table of effective field theories

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