On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states

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Abstract
In this work Onofri and Perelomov’s coherent states methods are extended to the recently introduced OSp(1/2) coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely, the OSp(1/2)/U(1) homogeneous superspace, which is clearly identified with a supercoadjoint orbit of OSp(1/2) by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein’s supersymplectic supermanifolds. More precisely, it is shown that its supersymplectic structure is completely determined in terms of SU(1,1)-invariant (but unrelated) Kähler 2-form and Kähler metric on the unit disc. This result leads to the definition of the notions of a super-Kähler supermanifold and a super-Kähler superpotential, the geometric structure of the former being encoded into the latter.
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