Soft Bootstrap and Supersymmetry

TL;DR

The paper develops the soft bootstrap framework, an on-shell method that uses soft subtracted recursion to constrain and classify EFTs of massless particles. It establishes a precise constructibility criterion that links low-energy theorems and extended shift symmetries to the existence of recursive representations, then applies it across scalars, fermions, vectors, and supersymmetric multiplets. Through extensive analysis of N=1/2 CP^1 nonlinear sigma models and Galileon-type theories, it reveals how soft behavior, SUSY Ward identities, and duality symmetries shape the allowed EFT landscape and its higher-derivative corrections. The work also connects on-shell recursion results with double-copy/KLT relations, offering a coherent on-shell perspective on exceptional EFTs, their symmetry structure, and their potential UV completions. These insights provide a practical, symmetry-driven route to map the space of consistent low-energy theories and guide future explorations of supersymmetric and Galileon-like constructions.

Abstract

The soft bootstrap is an on-shell method to constrain the landscape of effective field theories (EFTs) of massless particles via the consistency of the low-energy S-matrix. Given assumptions on the on-shell data (particle spectra, linear symmetries, and low-energy theorems), the soft bootstrap is an efficient algorithm for determining the possible consistency of an EFT with those properties. The implementation of the soft bootstrap uses the recently discovered method of soft subtracted recursion. We derive a precise criterion for the validity of these recursion relations and show that they fail exactly when the assumed symmetries can be trivially realized by independent operators in the effective action. We use this to show that the possible pure (real and complex) scalar, fermion, and vector exceptional EFTs are highly constrained. Next, we prove how the soft behavior of states in a supermultiplet must be related and illustrate the results in extended supergravity. We demonstrate the power of the soft bootstrap in two applications. First, for the N= 1 and N=2 CP^1 nonlinear sigma models, we show that on-shell constructibility establishes the emergence of accidental IR symmetries. This includes a new on-shell perspective on the interplay between N=2 supersymmetry, low-energy theorems, and electromagnetic duality. We also show that N=2 supersymmetry requires 3-point interactions with the photon that make the soft behavior of the scalar O(1) instead of vanishing, despite the underlying symmetric coset. Second, we study Galileon theories, including aspects of supersymmetrization, the possibility of a vector-scalar Galileon EFT, and the existence of higher-derivative corrections preserving the enhanced special Galileon symmetry. This is addressed by soft bootstrap and by application of double-copy/KLT relations applied to higher-derivative corrections of chiral perturbation theory.