A periodic table of effective field theories

By C. Cheung, K. Kampf, J. Novotný, Chia-Hsien Shen, J. Trnka. 2016

162 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Algebra and Number Theory, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eb8241083b02a96df5ed3fe150b4c4105e84b920

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In Algebra and Number Theory

C. Cheung

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

TASI Lectures on Scattering Amplitudes (2017, methodology): “To characterize the behavior in the soft limit, we define a soft degree σ [61, 62],”
Unifying relations for scattering amplitudes (2017, methodology): “The expression from color-ordered Feynman diagrams yields3 A(g1, g2, g3, g4) = n[12][34] p1p2 + n[23][41] p2p3 − (1)2 [(e1e2)(e3e4) + (e2e3)(e4e1)] + (e1e3)(e2e4) , (52) where the numerator of the cubic diagram is n[12][34] = n1234 − n2134 − n1243 + n2143 and n1234 = 1 4(e1e2)(e3e4)(p1p3)− (e2e3)(p3”
Operator bases, S-matrices, and their partition functions (2017, background): “Through requiring locality, and by further considering the behavior of scattering amplitudes in the soft limit, a systematic classification of Lorentz invariant single scalar EFTs in d < 6 dimensions has also been recently obtained [55, 56].”