Projective Superspace as a Double--Punctured Harmonic Superspace

TL;DR

The paper clarifies the relationship between $N=2$ harmonic and projective superspaces, arguing that projective superspace constitutes a minimal, double-punctured truncation of the harmonic framework. It demonstrates how polar (arctic) and tropical multiplets arise as natural projective realizations of harmonic analytic superfields, and shows how projective actions and propagators can be derived from harmonic-space constructions. A key result is that low-energy hypermultiplet actions in harmonic superspace reduce, under projective truncation, to a chiral–non-minimal nonlinear sigma model whose target space is the tangent bundle of a Kähler manifold, with a holomorphic Kähler potential governing the interaction. The work highlights the complementary strengths of the two formalisms and emphasizes the practical advantages of projective superspace for $N=1$ reductions and for guiding quantum calculations in $N=2$ theories.

Abstract

We analyse the relationship between the N=2 harmonic and projective superspaces which are the only approaches developed to describe general N=2 super Yang-Mills theories in terms of off-shell supermultiplets with conventional supersymmetry. The structure of low-energy hypermultiplet effective action is briefly discussed.