Noncommutative supergeometry and duality

Details Noncommutative supergeometry and duality Noncommutative supergeometry and duality

1999-12-22

arxiv.org/abs/hep-th/9912212v2

Lett.Math.Phys. 50 (1999) 309-321

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, Latex. Misprints corrected. Appendix added

Scientific paper

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 contains as a simplest case SO(d,d,{\bf Z})-duality of gauge theories on noncommutative tori.

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