Non-linear (3, 4, 1) multiplet of $\mathcal{N}=4$, $d=1$ supersymmetry as a semi-dynamical spin multiplet

Abstract

We consider a new type of $\mathcal{N}=4$, $d=1$ semi-dynamical multiplet based on the non-linear version of the mirror multiplet $(3,4,1)$, with the triplet of bosonic physical fields parametrizing a three-dimensional sphere $S^3$ of the radius $R$. The limit $R\to \infty$ amounts to the contraction $S^3\to {\mathbb{R}}^3$ and leads to the linear mirror multiplet $(3,4,1)$. Spin degrees of freedom described by a Wess-Zumino action specify a two-dimensional surface embedded in the sphere $S^3$. A pair of the examples considered correspond to the round and squashed ``fuzzy'' 2-spheres. We couple the squashed 2-sphere model to the dynamical mirror multiplet $(2,4,2)$. A notable feature of this coupling is the dependence of the squashing parameter on the bosonic fields $z,\bar{z}$ of the chiral multiplet.

1+17 pages