# An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry

## TL;DR

This paper develops a classification scheme for supersymmetric effective field theories with enhanced soft limits, focusing on exceptional algebras that produce maximum soft enhancements and using superspace inverse Higgs constraints.

## Contribution

It introduces a Lie-superalgebraic framework to classify supersymmetric EFTs with enhanced soft limits, extending on-shell methods to supersymmetric cases.

## Key findings

- Classified exceptional algebras for single Goldstone supermultiplets in 4D.
- Connected algebraic structures to soft weights of component fields.
- Provided a superspace approach to identify symmetry constraints in EFTs.

## Abstract

We present a novel approach to classify supersymmetric effective field theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These enhancements arise due to non-linearly realised symmetries on the Goldstone modes of such EFTs and we classify the algebras that these symmetries can form. Our main focus is on so-called exceptional algebras which lead to field-dependent transformation rules and EFTs with the maximum possible soft enhancement at a given derivative power counting. We adapt existing techniques for Poincar\'{e} invariant theories to the supersymmetric case, and introduce superspace inverse Higgs constraints as a method of reducing the number of Goldstone modes while maintaining all symmetries. Restricting to the case of a single Goldstone supermultiplet in four dimensions, we classify the exceptional algebras and EFTs for a chiral, Maxwell or real linear supermultiplet. Moreover, we show how our algebraic approach allows one to read off the soft weights of the different component fields from superspace inverse Higgs trees, which are the algebraic cousin of the on-shell soft data one provides to soft bootstrap EFTs using on-shell recursion. Our Lie-superalgebraic approach extends the results of on-shell methods and provides a complementary perspective on non-linear realisations.