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A periodic table of effective field theories
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 06 February 2017

A periodic table of effective field theories

  • Clifford Cheung1,
  • Karol Kampf2,
  • Jiri Novotny2,
  • Chia-Hsien Shen1 &
  • …
  • Jaroslav Trnka3 

Journal of High Energy Physics volume 2017, Article number: 20 (2017) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

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.

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Authors and Affiliations

  1. Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, U.S.A.

    Clifford Cheung & Chia-Hsien Shen

  2. Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Karol Kampf & Jiri Novotny

  3. Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA, U.S.A.

    Jaroslav Trnka

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Correspondence to Chia-Hsien Shen.

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ArXiv ePrint: 1611.03137

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Cheung, C., Kampf, K., Novotny, J. et al. A periodic table of effective field theories. J. High Energ. Phys. 2017, 20 (2017). https://doi.org/10.1007/JHEP02(2017)020

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  • Received: 27 November 2016

  • Revised: 25 January 2017

  • Accepted: 26 January 2017

  • Published: 06 February 2017

  • DOI: https://doi.org/10.1007/JHEP02(2017)020

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Keywords

  • Effective field theories
  • Scattering Amplitudes
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