Supersymmetry Breaking by Higher Dimension Operators

TL;DR

This work shows that higher-dimensional operators can trigger spontaneous SUSY breaking in N=1 theories and realize Volkov–Akulov-type goldstino dynamics across different multiplets. By studying chiral spinor, real linear, and complex linear multiplets, the authors demonstrate how auxiliary sectors can yield a goldstino without a sgoldstino and how a nontrivial scalar potential for propagating fields can arise. A key result is that in the SUSY-breaking vacuum the spectrum typically comprises a free chiral multiplet plus a constrained goldstino multiplet, with the goldstino sometimes being an auxiliary fermion that becomes dynamical. The complex linear multiplet, in particular, enables a consistent SUSY-breaking vacuum via a higher-dimensional operator where the sgoldstino decouples, and it provides a framework to couple to matter and gauge sectors, potentially extendable to supergravity.

Abstract

We discuss a supersymmetry breaking mechanism for N = 1 theories triggered by higher dimensional op- erators. We consider such operators for real linear and chiral spinor superfields that break superymmetry and reduce to the Volkov-Akulov action. We also consider supersymmetry breaking induced by a higher dimensional operator of a nonminimal scalar (complex linear) multiplet. The latter differs from the stan- dard chiral multiplet in its auxiliary sector, which contains, in addition to the complex scalar auxiliary of a chiral superfield, a complex vector and two spinors auxiliaries. By adding an appropriate higher di- mension operator, the scalar auxiliary may acquire a nonzero vev triggering spontaneous supersymmetry breaking. We find that the spectrum of the theory in the supersymmetry breaking vacuum consists of a free chiral multiplet and a constraint chiral superfield describing the goldstino. Interestingly, the latter turns out to be one of the auxiliary fermions, which becomes dynamical in the supersymmetry breaking vacuum. In all cases we are considering here, there is no sgoldstino mode and thus the goldstino does not have a superpartner. The sgoldstino is decoupled since the goldstino is one of the auxiliaries, which is propagating only in the supersymmetry breaking vacuum. We also point out how higher dimension operators introduce a potential for the propagating scalar of the theory.