Abstract
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, Z)-duality of gauge theories on noncommutative tori.
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Schwarz, A. Noncommutative Supergeometry and Duality. Letters in Mathematical Physics 50, 309–321 (1999). https://doi.org/10.1023/A:1007621011698
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DOI: https://doi.org/10.1023/A:1007621011698