Extended supersymmetry of semichiral sigma model in 4D

Abstract

Briefly: Using a novel $(1,1)$ superspace formulation of semichiral sigma models with $4D$ target space, we investigate if an extended supersymmetry in terms of semichirals is compatible with having a $4D$ target space with torsion. In more detail: Semichiral sigma models have $(2,2)$ supersymmetry and Generalized Kähler target space geometry by construction. They can also support $(4,4)$ supersymmetry and Generalized Hyperkähler geometry, but when the target space is four dimensional indications are that the geometry is restricted to Hyperkähler. To investigate this further, we reduce the model to $(1,1)$ superspace and construct the extra (on-shell) supersymmetries there. We then find the conditions for a lift to $(2,2)$ super space and semichiral fields to exist. Those conditions are shown to hold for Hyperkähler geometries. The $SU(2)\otimes U(1)$ WZW model, which has $(4,4)$ supersymmetry and a semichiral description, is also investigated. The additional supersymmetries are found in $(1,1)$ superspace but shown {\em not} to be liftable to a $(2,2)$ semichiral formulation.

arXiv comment23 pages. Resubmitted after compilation problems

References in corpus (12)

• Generalized Kahler manifolds and off-shell supersymmetry
• Complex Structures, Duality, and WZW-Models in Extended Superspace
• T-duality and world-sheet supersymmetry
• Properties of Semi-Chiral Superfields
• New N=4 Superfields and Sigma-models
• T-duality and Generalized Kahler Geometry
• Pseudo-hyperkahler Geometry and Generalized Kahler Geometry
• The generalized Kaehler geometry of N=(2,2) WZW-models
• Nonabelian Generalized Gauge Multiplets
• The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality
• Semichiral Sigma Models with 4D Hyperkaehler Geometry
• Off-shell N=(4,4) supersymmetry for new (2,2) vector multiplets

Cited by in corpus (4)

• Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
• Superspace Higher Derivative Terms in Two Dimensions
• Yano F structures and extended Supersymmetry
• Generalized Kahler structures on group manifolds and T-duality