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. An important ingredient in our analysis is inverse Higgs trees which systematically incorporate the requirements for the existence of inverse Higgs constraints. These are the algebraic cousin of the on-shell soft data one provides for soft bootstrapping EFTs. We perform full classifications for single scalar and multiple spin-1/2 fermion EFTs and present a thorough analysis for multiple scalars. 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 with non-linearly realised symmetries.
Highlights
Dirac-Born-Infeld1 (DBI) action [16, 17] where the amplitudes begin at quadratic order in psoft, and the Special Galileon [18] whose soft amplitudes begin at cubic order
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 turn to the case where Zmax = 1. We find it useful to separate the calculation into two sub-cases: in the first we do not allow any non-linear generators in the dilaton’s inverse Higgs tree, while in the second case we do allow for that vector generator which we denote as K
Summary
The first step is to incorporate the necessary inverse Higgs constraints at the level of the algebra, while satisfying Jacobi identities which involve two copies of translations. The second step is to demand the presence of canonical propagators in the resulting EFTs, which restricts the Lorentz representation of allowed non-linear generators in a very powerful way. This is possible since in the absence of the dilaton and tadpoles, the kinetic terms are the operators with the fewest powers of the field. The third step is to impose the final constraints from Jacobi identities
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