TY - JOUR

T1 - Nilpotent deformations of N = 2 superspace

AU - Ivanov, Evgeny

AU - Zupnik, Boris

AU - Lechtenfeld, Olaf

N1 - Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2004/2/1

Y1 - 2004/2/1

N2 - We investigate deformations of four-dimensional N = (1, 1) euclidean super-space 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.

AB - We investigate deformations of four-dimensional N = (1, 1) euclidean super-space 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.

KW - Extended Supersymmetry

KW - Non-Commutative Geometry

KW - Superspaces

UR - http://www.scopus.com/inward/record.url?scp=23044489742&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2004/02/012

DO - 10.1088/1126-6708/2004/02/012

M3 - Article

AN - SCOPUS:23044489742

VL - 8

SP - 331

EP - 346

JO - Journal of high energy physics

JF - Journal of high energy physics

SN - 1029-8479

IS - 2

ER -