Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-04-27
Nucl.Phys. B460 (1996) 362-378
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, Latex. Some references, discussions and comments (mainly in setion 4) and a note added
Scientific paper
10.1016/0550-3213(95)00640-0
We study the non-localization of extended worldsheet supersymmetry under T-duality, when the associated complex structure depends on the coordinate with respect to which duality is performed. First, the canonical transformation which implements T-duality is generalized to the supersymmetric non-linear $\sigma$-models. Then, we obtain the non-local object which replaces the complex structure in the dual theory and write down the condition it should satisfy so that the dual action is invariant under the non-local supersymmetry. For the target space, this implies that the supersymmetry transformation parameter is a non-local spinor. The analogue of the Killing equation for this non-local spinor is obtained. It is argued that in the target space, the supersymmetry is no longer realized in the standard way. The string theoretic origin of this phenomenon is briefly discussed.
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