Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-04-22
Nucl.Phys.B722:297-327,2005; Erratum-ibid.B747:464-465,2006
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, typos corrected in eqs. (3.15), (3.16); two commutation relations between supersymmetry and SU(2) operators added in
Scientific paper
10.1016/j.nuclphysb.2005.06.018
The ${\cal N}{=}8, 1D$ analytic bi-harmonic superspace is shown to provide a natural setting for ${\cal N}{=}8$ supersymmetric mechanics associated with the off-shell multiplet ${\bf (4, 8, 4)}$ . The latter is described by an analytic superfield $q^{1,1}$, and we construct the general superfield and component actions for any number of such multiplets. The set of transformations preserving the flat superspace constraints on $q^{1,1}$ constitutes ${\cal N}{=}8$ extension of the two-dimensional Heisenberg algebra {\bf h}(2), with an operator central charge. The corresponding invariant $q^{1,1}$ action is constructed. It is unique and breaks 1D scale invariance. We also find a one-parameter family of scale-invariant $q^{1,1}$ actions which, however, are not invariant under the full ${\cal N}{=}8$ Heisenberg supergroup. Based on preserving the bi-harmonic Grassmann analyticity, we formulate ${\cal N}{=}8, 1D$ supergravity in terms of the appropriate analytic supervielbeins. For its truncated version we construct, both at the superfield and component levels, the first example of off-shell $q^{1,1}$ action with local ${\cal N}{=}8, 1D$ supersymmetry. This construction can be generalized to any number of self-interacting $q^{1,1}$ .
Bellucci Stefano
Ivanov Evgeny
Sutulin Anton
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