Semichirals and Four Dimensional Geometry

Ulf Lindström

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arXiv · 1505.01360

Semichirals and Four Dimensional Geometry

Ulf Lindström

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Abstract

Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel description in $(1,1)$ superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra supersymmetry is only possible for hyperk\"ahler target geometry. A semichiral formulation of the $SU(2)\otimes U(1)$ WZW model is seemingly a counterexample to this. After deriving the extra supersymmetries of this model in $(1,1)$ superspace it is shown that they cannot be lifted to transformations of semichirals in $(2,2)$ superspace.

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Ulf Lindström. 2015-05-06. Semichirals and Four Dimensional Geometry. https://arxiv.org/abs/1505.01360

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