# An Algebraic Classification of Exceptional EFTs

## TL;DR

This paper classifies four-dimensional effective field theories with enhanced soft limits based on non-linearly realised symmetries, identifying a small set of exceptional theories including Dirac-Born-Infeld, Special Galileon, and Volkov-Akulov models.

## Contribution

It introduces an algorithm to derive all possible non-linear symmetry algebras for Goldstone modes and classifies the resulting exceptional EFTs with multiple scalars or fermions.

## Key findings

- Identified a small set of consistent algebras for Goldstone modes.
- Classified exceptional EFTs including Dirac-Born-Infeld, Galileon, and Volkov-Akulov.
- Extended the classification to theories with gauge vectors and scalar couplings.

## 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 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. 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.