On the Supersymplectic Homogeneous Superspace Underlying the OSp(1/2) Coherent States

Abstract

In this work we extend Onofri and Perelomov's coherent states methods to the recently introduced $OSp(1/2)$ coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely the homogeneous superspace $OSp(1/2)/U(1)$, 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, we show 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 allows us to define the notions of a superKähler supermanifold and a superKähler superpotential, the geometric structure of the former being encoded into the latter.

arXiv comment19 pgs, PlainTeX, Preprint CRM-1850

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