The Large Vector Multiplet underlies a new gauge multiplet in (2,2) supersymmetry, and gauging with it produces a beta-gamma system coupled to a sigma model.
Complex Structures, Duality, and WZW-Models in Extended Superspace
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abstract
We find the complex structure on the dual of a complex target space. For $N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the commutator of the left and right complex structures is {\em always} integrable, and hence the kernel is parametrized by chiral and twisted chiral superfield coordinates. We then analyze the particular case of $SU(2)\times SU(2)$, and are led to a new $N=2$ superspace formulation of the $SU(2)\times U(1)$ WZW-model.
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The Large Vector Multiplet and Gauging $(2,2)$ $\sigma$-models
The Large Vector Multiplet underlies a new gauge multiplet in (2,2) supersymmetry, and gauging with it produces a beta-gamma system coupled to a sigma model.