Sigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures

Abstract

We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.

20 pages; v2: significant corrections, clarifications, and reorganization; v3: discussion of supersymmetry vs twisted supersymmetry added, relevant signs corrected.

References in corpus (3)

• Generalized Hyperkaehler Geometry and Supersymmetry
• Linearizing Generalized Kahler Geometry
• Generalized Kahler geometry and gerbes

Cited by in corpus (11)

• Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
• A twistor sphere of generalized Kahler potentials on hyperkahler manifolds
• All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry
• Off-shell N=(4,4) supersymmetry for new (2,2) vector multiplets
• Semichiral Sigma Models with 4D Hyperkaehler Geometry
• Yano F structures and extended Supersymmetry
• Supersymmetric Sigma Model geometry
• Sigma models with non-commuting complex structures and extended supersymmetry
• T-duality on Almost Hermitian Spaces
• N=(4,4) supersymmetry and T-duality
• Semichirals and Four Dimensional Geometry