  We introduce a new topological sigma model, whose fields are bundle maps from
the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an
exact Courant algebroid over a target manifold. It generalizes simultaneously
the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations
of motion are satisfied, iff the corresponding classical field is a Lie
algebroid morphism. The Dirac Sigma Model has an inherently topological part as
well as a kinetic term which uses a metric on worldsheet and target. The latter
contribution serves as a kind of regulator for the theory, while at least
classically the gauge invariant content turns out to be independent of any
additional structure. In the (twisted) Poisson case one may drop the kinetic
term altogether, obtaining the WZ-Poisson sigma model; in general, however, it
is compulsory for establishing the morphism property.
