Abstract
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.
Highlights
JHEP05(2018)190 to the non-vanishing of the second commutator; the final commutator just expresses the Lorentz nature of the additional vector generator
We have discussed the existence of a fermionic symmetry akin to bosonic internal symmetries
This fermionic extension of Poincare is inequivalent to conventional supersymmetry and instead can be constructed from Inonu-Wigner contractions of superalgebras, starting either in four or in higher dimensions
Summary
The only non-trivial commutator is with Lorentz generators, reflecting the fact that S transforms as spin-1/2 This fermionic extension of Poincare is akin to an internal symmetry, and we will refer to it as internal supersymmetry. The coset combination λαQα is invariant under the algebra contraction together with the fermion small-field limit λα → λα/ω , with ω → ∞. One would expect the contracted algebras to only have non-linear representation, and internal supersymmetry cannot be restored as a linear transformation above some energy scale This theory has been shown not to admit unitary UV completions [26], similar to Galileons; instead, it could provide an alternative realization of fermion compositeness with specific LHC signatures, as discussed in [27, 28]. In the absence of Wess-Zumino terms, the fermion is derivatively coupled in all invariants, which implies that they give rise to second-order field equations and Ostrogradsky instabilities. A supersymmetric coupling to a healthy bosonic sector can remove the instability, as the example of the section demonstrates
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