An Algebraic Classification of Exceptional EFTs

Understand

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 Poincar\'{e} 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.