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We construct a two-dimensional topological sigma model whose target space isendowed with a Poisson algebra for differential forms. The model consists of anequal number of bosonic and fermionic fields of worldsheet form degrees zeroand one. The action is built using exterior products and derivatives, withoutany reference to any worldsheet metric, and is of the covariant Hamiltonianform. The equations of motion define a universally Cartan integrable system. Inaddition to gauge symmetries, the model has one rigid nilpotent supersymmetrycorresponding to the target space de Rham operator. The rigid and localsymmetries of the action, respectively, are equivalent to the Poisson bracketbeing compatible with the de Rham operator and obeying graded Jacobiidentities. We propose that perturbative quantization of the model yields acovariantized differential star product algebra of Kontsevich type. We commenton the resemblance to the topological A model.

2D sigma models and differential Poisson algebras