Nilpotent deformations of N=2 superspace

TL;DR

This paper explores nilpotent deformations of four-dimensional N=(1,1) superspace using harmonic superspace, introducing variants that preserve different amounts of supersymmetry and analyzing their effects on supersymmetric actions.

Contribution

It introduces and analyzes two types of nilpotent deformations of N=(1,1) superspace, expanding understanding of supersymmetry breaking and preservation in deformed superspaces.

Findings

Chiral nilpotent deformation preserves some supersymmetry and generalizes previous models.

Analytic nilpotent deformation maintains all supersymmetries but alters chirality.

Constructs non(anti)commutative Euclidean analogs of N=2 Maxwell and hypermultiplet actions.

Abstract

We investigate deformations of four-dimensional N=(1,1) euclidean superspace induced by nonanticommuting fermionic coordinates. We essentially use the harmonic superspace approach and consider nilpotent bi-differential Poisson operators only. One variant of such deformations (termed chiral nilpotent) directly generalizes the recently studied chiral deformation of N=(1/2,1/2) superspace. It preserves chirality and harmonic analyticity but generically breaks N=(1,1) to N=(1,0) supersymmetry. Yet, for degenerate choices of the constant deformation matrix N=(1,1/2) supersymmetry can be retained, i.e. a fraction of 3/4. An alternative version (termed analytic nilpotent) imposes minimal nonanticommutativity on the analytic coordinates of harmonic superspace. It does not affect the analytic subspace and respects all supersymmetries, at the expense of chirality however. For a chiral nilpotent deformation, we present non(anti)commutative euclidean analogs of N=2 Maxwell and hypermultiplet off-shell actions.