An Algebraic Classification of Exceptional EFTs

Abstract

We classify four-dimensional effective field theories (EFTs) with enhanced soft limits, which arise due to non-linearly realised symmetries on the Goldstone modes of such theories. We present an algorithm for deriving all possible algebras that can be non-linearly realised on a set of Goldstone modes with canonical propagators, linearly realised Poincaré symmetries and interactions at weak coupling. We then perform a full classification of the cases with multiple scalars or multiple spin-$1/2$ fermions as the Goldstone modes. In each case there are only a small number of algebras consistent with field-dependent transformation rules, leading to the class of exceptional EFTs including the scalar sector of Dirac-Born-Infeld, Special Galileon and Volkov-Akulov theories. We also discuss the coupling of a $U(1)$ gauge vector to the exceptional scalar theories, showing that there is a Special Galileon version of the full Dirac-Born-Infeld theory. This paper is part I in a series of two papers, with the second providing an algebraic classification of supersymmetric theories.

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Cited by in corpus (21)

• The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales
• Shift symmetries, soft limits, and the double copy beyond leading order
• Exceptional scalar theories in de Sitter space
• Symmetric Scalars
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
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• Soft Phonon Theorems
• Hidden Conformal Invariance of Scalar Effective Field Theories
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• Fermionic Shift Symmetries in (Anti) de Sitter Space
• Exceptional nonrelativistic effective field theories with enhanced symmetries
• On the Conformal Symmetry of Exceptional Scalar Theories
• New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation
• Soft unification of exceptional effective field theories in de Sitter space