Noncommutative supergeometry, duality and deformations

Details Noncommutative supergeometry, duality and deformations Noncommutative supergeometry, duality and deformations

2002-10-28

arxiv.org/abs/hep-th/0210271v2

Nucl.Phys. B650 (2003) 475-496

Physics

High Energy Physics

High Energy Physics - Theory

Extended version of hep-th/9912212

Scientific paper

10.1016/S0550-3213(02)01088-X

We introduce a notion of $Q$-algebra that can be considered as a generalization of the notion of $Q$-manifold (a supermanifold equipped with an odd vector field obeying $\{Q,Q\} =0$). We develop the theory of connections on modules over $Q$-algebras and prove a general duality theorem for gauge theories on such modules. This theorem containing as a simplest case $SO(d,d,{\bf Z})$-duality of gauge theories on noncommutative tori can be applied also in more complicated situations. We show that $Q$-algebras appear naturally in Fedosov construction of formal deformation of commutative algebras of functions and that similar $Q$-algebras can be constructed also in the case when the deformation parameter is not formal.

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