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. 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.

We investigate the interplay between moduli dynamics and inflation, focusing on the KKLTscenario and cosmological α-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for α-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The gravitino mass is independent from the inflationary scale with no fine-tuning of the parameters. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.improves the decoupling of the two physical scales. This so-called KL model and its coupling to inflation was further explored in [5,6]. arXiv:1607.08231v2 [hep-th]

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 Poincaré 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. 1 d.roest@rug.nl 2 d.stefanyszyn@rug.nl 3 p.j.werkman@rug.nl 1 Note that this simple connection between symmetries and enhanced soft limits does not apply to gauge theories, where gauge symmetries can be thought of as an infinite number of coordinate dependent symmetries, but is certainly applicable to scalar and spin-1/2 fermions. We will comment on gauge theories in section 5.1 compatible with a canonical propagator. This is important when understanding the soft behaviour of a dilaton, for example, where once we canonically normalise all terms in all transformation rules are field-dependent 2 , see e.g. [15]. It does therefore not fit into the above classification but it is known that the dilaton has σ = 0 soft behaviour [16][17][18].However, the soft amplitude bootstrap is not the only way of classifying these special EFTs without reference to Lagrangians. Any symmetries which are non-linearly realised on the fields must form a consistent Lie-algebra with the assumed linearly realised symmetries. One can therefore ask which Lie-algebras are consistent within the framework of the coset construction for non-linear realisations [19][20][21] augmented with the crucial inverse Higgs phenomenon 3 [22]. For scalar EFTs Lie-algebraic approaches have been presented in [23,24] while in [25] these methods were used to prove that a gauge vector cannot be a Goldstone mode of a spontaneously broken space-time symmetry without introducing new degrees of freedom. This implies that the Born-Infeld (BI) vector is not special from the perspective of non-linear symmetries and enhanced soft limits (the same result was found in [8] where it was shown that the BI vector has a vanishing soft weight).Recently, we presented an algorithm f...

The dynamics of the Goldstino mode of spontaneously broken supersymmetry is universal, being fully determined by the non-linearly realized symmetry. We investigate the small-field limit of this theory. This model non-linearly realizes an alternative supersymmetry algebra with vanishing anti-commutators between the fermionic generators, much like an internal supersymmetry. This Goldstino theory is akin to the Galilean scalar field theory that arises as the small-field limit of Dirac-Born-Infeld theory and non-linearly realizes the Galilean symmetry. Indeed, the small-field Goldstino is the partner of a complex Galilean scalar field under conventional supersymmetry. We close with the generalization to extended internal supersymmetry and a discussion of its higher-dimensional origin.

CONTENTS function of space-time, rather than a (possibly infinite) series of constant coefficients. The former are proper gauge redundancies, the latter make up the large gauge transformations.